Document RjM6En8brRz2yBXG8Kor1DoKn

FLOW OF FLUIDS THROUGH VALVES, FITTINGS, AND PIPE By (he Engineering Division Crane Co., Chicago Copyright. 1957--Crane Co. All rights reserved. This publication is fully protected by copyright and nothing that appears in it may be re printed, either wholly or in part, without special permission. Founded by R. T. Crane 1855 CRANE CO. . v"~ 836 S. Michigan Avenue Chicago 5, Illinois Technical Paper No. 410 PRINTED IN U. 5. A. (Third Printing) Price $10.00 CRANE CO___________ GENERAL OFFICES 836 5. Michigan Av.nva, Chicago 5 Cable Address: Cranecay--Chicago . MANUFACTURING PLANTS Chicago, ill. -- Chattanooga, Ttnn. Trenton, N. J. --Colton, Calif. export New York, San Antonio, and San Francisco Branches 1 t 5 CRANE BRANCHES ALABAMA BIRMINGHAM (3), 2 South 20th St. MOBILE (3). 300 N. Royal ARIZONA PHOENIX, 233 S. First Ave. TUCSON, 35 Toole Ave. ARKANSAS FT. SMITH,221 South 9th St LITTLE ROCK, 1000 E, Second SL KANSAS TOPEKA, 132 No. Kansas Ave. WICHITA (I), 624 E. 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Trafford Park BRISTOL (1), 19 Colston St BRENTFORD, Great West Road SCOTLAND t C IOWA DAVENPORT (8), 217 E. Second St NORTH DAKOTA FARGO*, 1441 4th Avenue, North OSHKOSH, 135 Market St WYOMING GLASGOW, 94-100 Clyde Ferry St Anderston In addition to Crone Branch Houses, Who/e- V/ '(Crane Company of Minnesota) MINOT*, Highways 2 and 52, West CASPER (5), 802 East "C" St saIon in all major markets till Crane products. FOREWORD The more complex industry becomes, the more vital becomes the role played by fluids in the industrial machine. One hun dred years ago water was the only impor tant fluid which was conveyed from ope point to another in pipe. Today, almost every conceivable fluid is handled in pipe during its production, processing, transpor tation, or utilization. The age of atomic energy and rocket power has added fluids such as liquid metals .... i.e., sodium, po tassium, and bismuth, as well as liquid oxygen, nitrogen, etc.... to the list of more common fluids such as oil, water, gases, acids, and liquors that are being trans ported in pipe today. Nor is the transpor tation of fluids the only phase .of hydrau lics which warrants attention now. Hy draulic and pneumatic mechanisms are used extensively for the controls of modern aircraft, sea-going vessels, automotive equipment, machine tools, earth-moving and road-building machines, and even in scientif ; laboratory equipment where pre cise control of fluid flow is required. So extensive are the applications of hydrau lics and fluid mechanics that almost every engineer has found it necessary to famil iarize himself with at least the elementary laws of fluid flow. To satisfy a demand for a simple and practical treatment of the subject of flow in pipe, Crane Co. published in 1935, a booklet entitled Flow of Fluids and Heat Transmission. A revised edition on the subject of Flow of Fluids Through Valves, Fittings, and Pipe was published in 1942. That this work was immediately acclaimed by both practical and scientific engineers..wass indicated by its world-wide circulatiorr afid the many favorable com ments received: The appearance of much new and useful data on the subject has made the present revision necessary. In order to obtain the latest information, Crane Co. sponsored a fellowship at Armour Research Foundation under the direction of Dr. V. L. Streeter. Mr. W. G. Kautz, recipient of the fellowship, com- piled much of the data upon which the present revision is based. Development and arrangement of these data to the form in which they are presented, as well as the analysis of extensive Crane Laboratory and field test data, required the extensive effort of Crane Engineers for a period of several years. The chief endeavor in the preparation of the present edition has been to present the newest available information on the flow of fluids, in summarized form, and to include all the auxiliary data necessary to the solu tion of any but the most unusual fluid flow problems. As in the 1942 edition, nomographs are included for the use of those engineers who prefer graphical methods of solving some of the more simple problems. However, the number.of nomographs.has been considerably reduced by avoiding duplication; at the same time, their range of application has- been ex panded. .; T -* The general arrangement of the book has been changed to present the theory in Chapters. 1 and 2 . .. . practical application to flow problems in Chapters 3 and 4 ... . physical properties of fluids and flow char acteristics of valves, fittings, and pipe in Appendix A . . . . and conversion units and other useful engineering data in Appendix B. Furthermore, a page numbering system has been adopted that will facilitate future revisions of individual chapters without affecting others. ' Most of the data on flow through valves and fittings were obtained by carefully conducted experiments in the Crane Engi neering Laboratories. Liberal use has been made, however, of other reliable sources of data on this subject and due credit has been given these sources in the text. The bibliography of references will' provide a source for further study of the subject presented. CRANE CO. ) t I S: iif i t l Table of Contents . CHAPTER 1 CHAPTER 2 Theory of Flow in Pipe page Introduction.................................................................. 1-1 Physical Properties of Fluids............................. -..... 1-2 Viscosity........................................................ ......... 1-2 Weight density ...................................................... 1-3 Specific volume...................................................... 1-3 Specific gravity...................................................... 1-3 Nature of Flow in Pipe-- Laminar and Turbulent............................................... 1-4 Mean velocity of flow............................................ 1-4 Reynolds number..................................................... 1-4 Hydraulic radius.................................................... 1--4 General Energy Equation-- Bernoulli's Theorem.................................................. 1-5 Measurement of Pressure............................................ 1-5 Darcy's Formula-- General Equation for Flow of Fluids....................... 1-6 Friction factor........................................................ 1-6 Effect of age and use on pipe friction................. 1-7 , Principles of Compressible Flow in Pipe................. 1-7 Complete isothermal equation.............................. 1-8 Simplified compressible flow-- gas pipe line formula........................................ 1-8 Other commonly used formulas, for compressible flow in long pipe lines............... 1-8 Comparison of formu' .s for compressible flow in pipe lines......................... 1-8 Limiting flow of gases and vapors....................... 1-9 Steam--General Discussion...................................... 1-10 -- " CHAPTER 3 -- Flow of Fluids Through Valves and Fittings Page Introduction.................................................................. 2-1 Types of Valves and Fittings Used in Pipe Systems.................................................. 2-2 Pressure Drop Chargeable to Valves and Fittings................................................ 2-2 Crane Flow Tests........................................................ 2-3 Relationship of Pressure Drop to Velocity of Flow.................................................... 2-7 Resistance Coefficient K, Equivalent Length L/D, and Flow Coefficient Cy.................................... 2-8 Relationship of Equivalent Length L/D and Resistance Coefficient K to the Inside Diameter of Connecting Pipe......................... 2-10 Valves with Gradually Increased Ports.... .............. 2-10 Effect of End Connections......................................... 2-10 Laminar Flow Conditions.......................................... 2-11 Basis for Design of Charts for Determining Equivalent Length, Resistance Coefficient, and Flow Coefficient.................................................... 2-11 Resistance of Bends.................................................... 2-12 Other Resistances to Flow.......................................... 2-13 Flow Through Nozzles and Orifices......................... 2-14 Liquids, gases, and vapors............ ........................ 2-14 Maximum flow of compressible fluids in a nozzle................................................ 2-15 Flow through short tubes...................................... 2-15 Discharge of Fluids Through Valves, Fittings, and Pipe Liquid flow ............................................................ 2-15 Compressible flow.................................................. 2-15 Formulas and Nomographs for Flow Through Valves, Fittings, and Pipe page Introduction ................................................................ 3-1 Summary of Formulas..................................... 3-2 to 3-5 Formulas and Nomographs for Liquid Flow Velocity .................................................................... 3-6 Reynolds number; friction factor for 1 clean steel and wrought iron pipe................... 3-8 Pressure drop for turbulent flow........................... 3-10 Pressure drop for laminar flow............................. 3-12 Flow through nozzles and orifices....................... 3-14 Formulas and Nomographs for Compressible Flow Velocity.................................................................... 3-16 Reynolds number; friction factor for clean steel and wrought iron pipe................... 3-18 Pressure drop........................................................... 3-20 Simplified flow formula........................................... 3-22 Flow through nozzles and orifices....................... 3-24 ------------ CHAPTER 4 Examples of Flow Problems page Introduction.................................................................. 4-1 Reynolds Number and Friction Factor for Pipe Other than Steel or Wrought Iron................... 4-1 Determination of Valve Resistance in L, L/D, K, and Flow Coefficient Cv............................... 4-2 Check Valves--Determination of Size..................... 4-3 Laminar Flow in Valves, Fittings, and Pipe........... 4-4 Pressure Drop and Velocity in Piping Systems ...................................................... 4-6 Pipe Line Flow Problems........................................... 4--10 Discharge of Fluids from Piping Systems............... 4-12 Flow Through Orifice Meters...................................4-15 Application of Hydraulic Radius to Flow Problems................................... 4-16 Determination of Boiler Capacity............................. 4-18 ttf ' ' A < APPENDIX A APPENDIX B Physical Properties of Fluids and Flow Characteristics of Valves, Fittings, and Pipe ' page Introduction ................................................................ A-l Engineering Data page Introduction ................................................................ B-l Equivalent Volume and Weight Flow Rates of Compressible Fluids........................ B-2 Physical Properties of Fluids . Viscosity of steam ............................................... A-2 Viscosity of water ............................................... A-3 Viscosity of liquid petroleum products............. A-3 Viscosity of various liquids .............................. A-4 Viscosity of gases and hydrocarbon vapors..... A-S Viscosity of refrigerant vapors ......................... A-S Physical properties of water................................. A-6 Specific gravity--temperature relationship for petroleum oils....................... A-7 Weight density and specific gravity of various liquids............................... A-7 Physical properties of gases................................. A-8 Volumetric composition and specific gravity of gaseous fuels.......................A-8 Steam--values of k.................................._............ A-9 / Weight density and specific ' volume of gases and vapors............................. A--10 Properties of saturated steam............................... A-12 Properties of superheated steam........................... A-16 Equivalents of Viscosity Absolute ................................................................ B-3 Kinematic .............................................................. B-3 Kinematic and Saybolt Universal...................... B-4 Kinematic and Saybolt Furol.............................. B-4 Kinematic, Saybolt Universal, Saybolt Furol, and Absolute.......................... B-5 Saybolt Universal Viscosity Chart........................... B-6 Equivalents of Degrees API, Degrees Baume, Specific Gravity, Weight Density, and Pounds per Gallon............... B-7 Steam Data Boiler capacity...................................................... B-8 Horsepower of an engine...................................... B-8 Ranges in steam consumption by prime movers............................................. B-8 Power Required for Pumping................................... B-9 Flow Characteristics of Nozzles and Orifices Flow coefficient C for nozzles............................... A-19 Flow coefficient C for square edged orifices...................................... A-19 Net expansion factor Y for compressible flow....................................... A-20 Critical pressure ratio, r0 for compressible flow....................................... A-21 Flow Characteristics of Pipe, Valves, and Fittings Net expansion factor Y for compressible flow through pipe to a larger flow area....... A-22 Relative roughness of pipe materials and friction factor for complete turbulence........... A-23 Friction factors for- ' any type of commercial pipe........................... A-24 Friction factors, for clean commercial steel and wrought iron pipe....... A-2S Resistance in pipt due to sudden enlargements and contractions........... A-26 Resistance in pipfeA.- . - due to pipe entrance and exit......................... A-26 Resistance of 90 degree bends............... ............. A-27 Resistance of miter bends.......................................A-27 Equivalents (General) ' / - Measure............................................................... . B-10 Weight1......................................... '......................... B-10 Velocity .................................................................. B-10 Density .................................................................. B-10 Physical constants................................................ B-10 Temperature .......................................................... B-10 Prefixes .................................................................. B--10 Liquid measures andweights........:....................... B-ll Pressure and head.................................................. B-ll Four-Place Logarithms toBase 10............................. B-12 Flow Through Schedule 40 Steel Pipe Water............................ ........................................ B-14 Air .......................................................................... B--15 Commercial Wrought Steel Pipe Data Schedules 10 to 160............................................... B-16 Standard, extra strong, and double extra strong................................... B-l8 -- APPENDIX C -- " , Types of valves (sectional illustrations)........... A--28 Bibliography ' Schedule (thickness) of steel pipe used in obtaining resistance of valves and fittings of various pressure classes............... A-30 Representative equivalent length (L/D) in pipe diameters of valves and fittings...........,. A-30 page Bibliography .............................................................. C--1 Equivalent lengths L and L/D and resistance coefficient K............................. A-31 Equivalents of resistance coefficient K and flow coefficient Cr..................................... A-32 I Nomenclature Nomenclature .see next page i t ( hH i` i i Nomenclature Unless otherwise stated, all symbols used in this book are defined as follows: fi A = cross sectional area of pipe or orifice, in R = individual gas constant = MR/M = square feet 1544/M = cross sectional1 area of pipe or orifice, in Re = Reynolds number square inches rc = critical pressure ratio for compressible flow B = rate of flow in barrels-(42 gallons) per hour S = specific gravity of liquids relative to water, C = flow coefficient for .orifices and nozzles both at standard temperature (60 F) = discharge coefficient corrected for vel S,, = specific gravity of a gas relative to air = ocity of approach = C,,/v i-(d0M)4 the ratio of the molecular weight of the C,t = discharge coefficient for orifices and nozzles gas to that of air l Cy = flow coefficient for valves; expresses flow T = absolute temperature, in degrees Rankine rate in gallons per minute of 60 F water (460 + t) with 1 .o psi pressure drop across valve t = temperature, in degrees Fahrenheit = Q V /./(62.4AP) D = internal diameter of pipe, in feet V = specific volume of fluid, in cubic feet per pound d = internal diameter of pipe, in inches V = mean velocity of flow, in feet per minute e = base of natural logarithm = 2.718 Va = volume, in cubic feet / = friction factor in formula hL =fL v2/D 2g v = mean velocity of flow, in feet per second g = acceleration of gravity = 32.2 feet per second per second v, = sonic (or critical) velocity of flow of a gas, in feet per second H = total head, in feet of fluid W = rate of flow, in pounds per hour h = static pressure head existing at a point, in feet of fluid h, = total-heat of steam, in Btu per pound hi = loss of static pressure head due to fluid flow, in feet of fluid ha = static pressure head, in inches of water w = rate of flow, in pounds per second wa = weight, in pounds x -- percent quality of steam = 100 minus per cent of moisture V = net expansion factor for compressible flow through orifices, nozzles, or pipe K = resistance coefficient or velocity head loss in the formula, hL = Kv2/zg Z = potential head or elevation above reference level, in feet k *= ratio of specific heat at constant pressure to specific heat at constant volume = cp/cc L = length of pipe, in feet '' L/D = equivalent length of a resistance to flow, in pipe diameters Subscripts (0) . . indicates orifice conditions unless other wise specified (1) . . indicates inlet or upstream conditions unless otherwise specified = length of pipe, in miles M = molecular weight (2) . . indicates outlet or downstream conditions unless otherwise specified MR = universal gas constant = 1544 (100) . refers to 100 feet of pipe = exponent in equation for polytropic change (p'Vna = constant) P = pressure, in pounds per square inch gauge P' = pressure, pounds per square inch absolute Greek Letters Dalta A = differential between two points (see page i-f for diagram showing relation ship between gauge and absolute pressure) Epsilon P' = pressure, in pounds per square foot absolute Q = rate of flow, in gallons per minute e = absolute roughness or effective height of pipe wall irregularities, in feet i q = rate of flow, in cubic feet per second at flowing conditions q' = rate of flow, in cubic feet per second at Rho p = weight density of fluid, pounds per cubic ft p' = density of fluid, grams per cubic centimeter standard conditions (14.7 psia and 60F) Mu q'd = rate of flow, in millions of standard cubic feet per day, MMscfd P = absolute (dynamic) viscosity, in centipoise pe -- absolute viscosity, in pound mass per foot q\ = rate of flow, in cubic feet per hour at stand ard conditions (14.7 psia and 60F), scfh second or poundal seconds per sq foot p'e -- absolute viscosity, in slugs per foot second qm = rate of flow, in cubic feet per minute at or pound force seconds per square foot flowing conditions Nu q'm = rate of flow, in cubic feet per minute at std. conditions (14.7 psia and 60F), scfm v = kinematic viscosity, in centistokes v' = kinematic viscosity, square feet per second ~ uum r The most commonly employed method of transport ing fluid from one point to another is to force the fluid to flow through a piping system. Pipe of cir cular section is most frequently used because that shape offers not only greater structural strength, but also greater cross sectional area per unit of wall sur face than any other shape. Unless otherwise stated, the word "pipe" in this book will always refer to a closed conduit of circular section and constant internal diameter; Only a few special problems in fluid mechanics .... laminar flow in pipe, for example .... can be entirely solved by rational mathematical means; all other problems require methods of solution which rest, at least in part, on experimentally determined coeffi cients. Many empirical formulas have been proposed for the problem of flow in pipe, but these are often extremely limited and can be applied only when the conditions of the problem closely approach the conditions of the experiments from which the for mulas were derived. Because of the great variety of fluids being handled in modem industrial processes, a single equation which can be used for the flow of any fluid in pipe offers obvious advantages. Such an equation is the Darcy* formula. The Darcy formula can be derived rationally by means of dimensional analysis; how ever, one variable in the formula .... the friction factor___ must be determined experimentally. This formula has a wide application in the field of fluid mechanics and is used extensively throughout this paper. The Darcy formula is also known as the Weisbach formula or the DarcyWeisbach formula; also, as the Fanning formula, sometimes modified so that the friction factor is one-fourth the Darcy friction factor. i j 1 -2 _ . . I *ii uliaiHeMiiEidli'i'fci CHAPTER 1 - THEORY OF FLOW IN PIPE CRANE Physical Properties of Fluids The solution of any flow problem requires a knowl second and is equivalent to 100 centistokes. edge of the physical properties of the fluid being handled. Accurate values for the properties affecting the flow of fluids . . . namely, viscosity and weight v (centistokes) = ft_____ (centipoise) p' (grams per cubic cm) M_ S density . . . have been established by-many authori ties for all commonly used fluids and many of these data are-presented in the various tables and charts in Appendix A. By definition, the specific gravity, S, in the fore going formula is based upon water at a temperature of 4 C (39.2 F), whereas specific gravity used throughout this paper is based upon water at 60 F. Viscosity: Viscosity expresses the readiness with which a fluid flows when it is acted upon by an ex In the English system, kinematic viscosity has dimensions of square feet per second. ternal force. The coefficient of absolute viscosity Factors for conversion between metric and English or, simply, the absolute viscosity of a fluid, is a system units of absolute and kinematic viscosity are v. measure of its resistance to internal deformation or given on page B-3 of Appendix B. ! shear. Molasses is a highly viscous fluid; water is i. comparatively much less viscous; and the viscosity The measurement of the absolute viscosity of fluids of gases is quite small compared to that of water. (especially gases and vapors) requires elaborate equipment and considerable experimental skill. On Although most fluids are predictable in their vis the other hand, a rather simple instrument can be cosity, in some, the viscosity depends upon the used for measuring the kinematic viscosity of oils previous working of the fluid. Printer's ink, wood and other viscous liquids. The instrument adopted pulp slurries, and catsup are examples of fluids as a standard in this country is the Saybolt Universal possessing such thixotropic properties of viscosity. Viscosimeter. In measuring kinematic viscosity Considerable confusion exists concerning the units used to express viscosity; therefore, proper units must be employed whenever substituting values of viscosity into formulas. In the C.G.S. (centimeter, gr< n, second) or metric system, the unit of absolute with this instrument, the time required for a small volume of liquid to flow through an orifice is deter mined; consequently, the "Saybolt viscosity" of the liquid is given in seconds. For very viscous liquids, the Saybolt Furol instrument is used. viscosity is the poise which is equal to 100 centi- Other viscosimeters, somewhat similar to the Saybolt poise. The poise has the dimensions of dyne seconds but not used to any extent in this country, are the per square centimeter or of grams per centimeter Engler, the Redwood Admiralty, and the Redwood. second. It is believed that less confusion concerning The relationship between Saybolt viscosity and units will prevail if the centipoise is used exclusively kinematic viscosity is shown on page B-4; equiva as the unit of viscosity. For this reason, and since lents of kinematic, Saybolt Universal, Saybolt Furol, i. most handbooks and tables follow the same pro and absolute viscosity can be obtained from the cedure, all viscosity data in this paper are expressed chart on page B-5. in centipoise. 4 The ASTM standard viscosity temperature chart for The English units commonly employed are "slugs per liquid petroleum products, reproduced on page B-6, I foot second" or "pound force seconds per square is used to determine the Saybolt Universal viscosity foot"; however, "pound mass per foot second" or of a petroleum product at any temperature when the "poundal seconds per square foot" may also be en viscosities at two different temperatures are known. countered. The viscosity of water at a temperature The viscosities of some of the most common fluids are of 68 F is: . given on pages A-2 to A-5. It will be noted that, i M= (o.oi poise o.oi gram per cm second with a rise in temperature, the viscosity of liquids decreases, whereas the viscosity of gases increases. The effect of pressure on the viscosity of liquids and o.oi dyne second per sq cm perfect gases is so small that it is of no practical Me = fo.ooo 672 pound mass per foot second \0.000 672 poundal second per square foot / Me -- f0.000 0209 slug per foot second \0.000 0209 pound force second per square ft interest in most flow problems. Conversely, the viscosity of saturated, or only slightly superheated, vapors is appreciably altered by pressure changes, as indicated on page A-2 showing the viscosity of steam. Unfortunately, the data on vapors are incomplete Kinematic viscosity is the ratio of the absolute vis and, in some cases, contradictory. Therefore, it is cosity to the mass density. In the metric system, expedient when dealing with vapors other than the unit of kinematic viscosity is the stoke. The steam to neglect the effect of pressure because of the stoke has dimensions of square centimeters per lack of adequate data. 'Actually the viscosity of water at 68 F 1' I 00< centipoise. sssssssm `d' CRANE CHAFTtt l-THlO*y"Of HOW IN'FIFE 1-3 Physical Properties of Fluids"-- continued Weight density, specific volume, and specific gravity: The weight density or specific weight of a substance is its weight per unit volume. In the English system of units, this is expressed in pounds per cubic foot and the symbol designation-used in this paper is p (Rho). In the metric system, the unit is grams per cubic centimeter and the symbol designation used is p' (Rho prime). The specific volume V, being the reciprocal of the weight density, is expressed in the English system as the number of cubic feet of space occupied by one pound of the substance, thus: V= i P ' Computations in the metric system are not com monly referred to in terms of specific volume; how ever, the number of cubic centimeters, per gram of a substance can readily be expressed as the reciprocal of the weight density, that is: p' ' The variations in weight density as well as other properties of water with changes in temperature are shown on page A-6. The weight densities of other common liquids are shown on page A-7. Unless very high pressures are being considered, the effect of pressure on the weight of liquids is of no practical importance in flow problems. In steam flow computations, the reciprocal of the weight density, which is the specific volume, is com monly used; these values are listed in the steam tables shown on pages A-12 to A-18. A chart for de termining the weight density and specific volume of gases is given on page A-l 1. Specific gravity is a relative measure of weight den sity. Since pressure has an insignificant effect upon the weight density of liquids, temperature is the only condition that must be considered in designat ing the basis for specific gravity. The specific grav ity of a liquid is its weight density at 60 F (unless otherwise specified) to that of water at standard temperature, 6o F. ( any liquid at 6o F, 1 ,, _ p (unless otherwise specified/ ~ p (water at 6o F) A hydrometer can be used to measure the specific gravity of liquids directly. Three hydrometer scales are common in this country.... the API scale which is used for oils___ and the two Baume scales, one for liquids heavier than water and one for liquids lighter than water. The relationship between the hydrometer scales and spi. ific gravity are: For oils, ^6oF/6oF)-|>[;;^.m For liquids lighter than water, The weight densities of gases and vapors, however, are greatly altered by pressure changes. For the socalled "perfect" gases, the weight density can be computed from the formula: 5(6oF/6oF)-|30 + <^B55S For liquids heavier than water, ' _ 44J* p " RT S(6oF/6oF The individual gas constant R is equal to the univer sal gas constant, MR = 1544, divided by the molecu lar weight of the gas, . ' ' Values of R, as well as other useful gas constants, are given on page A-8. The weight density of air for various conditions of temperature and pressure can be found on page A-10. . For convenience in converting hydrometer readings to more useful units, refer to the table shown on page B-7. The specific gravity of gases is defined as the ratio of the molecular weight of the gas to that of air, and as the ratio of the individual gas constant of air to that of the gas. . n _ R (air) _ M (gas) * R(gas) M (air) / -** -a*' 1-4 CHAPTER 1 - THEORY OF FlOW JN PIPE_______________________________________________________________________________________ CRANE I Nature of Flow in Pipe -- Laminar and Turbulent 1HHH ' Figure 1-1 Laminar Flow Actual photograph of colored fllamonti being carried along undisturbed by a stream of water. Figure 1-2 Flow In Critical Zone, Between Laminar and Transition Zones At the critical velocity, the filaments begin to break up, indicating flow Is becoming turbulent. Figure 1-3 Turbulent Flew This illustration shows the turbulence in the stream completely dispersing the colored filaments a short distance downstream from the point of injection. A simple experiment (illustrated above) will readily "Reasonable" velocities for use in design work are show there are two entirely different types of flow given on pages 3-6 and 3-16. J in pipe. The experiment consists of injecting small streams -of a colored fluid into a liquid flowing in Reynolds number: The work of Osborne Reynolds a glass pipe and observing the behavior of these has shown that the nature of flow in pipe .... that colored streams at different sections downstream is, whether it is laminar or turbulent .... depends from their points of injection. on the pipe diameter, the density and viscosity of the flowing fluid, and the velocity of flow. The If the discharge or average velocity is small, the numerical value of a dimensionless combination of streaks of colored fluid flow in straight lines, as these four variables, known as the Reynolds num shown in Figure 1-1. As the flow rate is gradually ber, may be considered to be the ratio of the dynamic increased, these streaks will continue to flow in forces of mass flow to the shear stress due to vis straight lines until a velocity is reached when the cosity. Reynolds number is: streaks will waver and suddenly break into diffused patterns as shown in Figure 1-2. The velocity at which ti is occurs is called the "critical velocity". At velocities higher than "critical", the filaments R,, e = Dvo ------- lit Equation 1-2 (For other forms of this equation, see page 3-2.) are dispersed at random throughout the main body of For engineering purposes, flow in pipes is usually the fluid, as shown in Figure 1-3. considered to be laminar if the Reynolds number is The type of flow which exists at velocities lower than "critical" is known as laminar flow and, some times, as viscous or streamline flow. Flow of this nature is characterized by the gliding of concentric cylindrical layers past one another in orderly fash ion. Velocity of the fluid is at its maximum at the pipe axis and decreases sharply to zero at the wall. less than 2000, and turbulent if the Reynolds number is greater than 4000. Between these two values lies the "critical zone" where the flow .... being laminar, turbulent, or in the process of change, depending upon many possible varying conditions .... is unpredictable. Careful experimentation has shown that the laminar zone may be made to terminate at a Reynolds number as low as 1200 or extended as At velocities greater than "critical", the flow is tur bulent. In turbulent flow, there is an irregular high as 40,000, but these conditions are not expected to be realized in ordinary practice. random motion of fluid particles in directions trans Hydraulic radius: Occasionally a conduit of non verse to the direction of the main flow. The velocity distribution in turbulent flow is more uniform across the pipe diameter than in laminar flow. Even though a turbulent motion exists throughout the greater portion of the pipe diameter, there is always a thin layer of fluid at the pipe wall .... known as the "boundary layer" or "laminar sub-layer" .... which is moving in laminar flow. circular cross section is encountered. In calculating the Reynolds number for this condition, the equiva lent diameter (four times the hydraulic radius) is sub stituted for the circular diameter. Use friction factors given on pages A-24 and A-25. . , area of flowing fluid hydraulic radius = wetted perfmeTiT Mean velocity of flow: The term "velocity", unless otherwise stated, refers to the mean, or average, velocity at a given cross section, as determined by the continuity equation for steady state flow: q _ w _ wV A -- ~Ap- ~ ~A~ Equation l-l (For nomenclature, see page preceding Chapter 1) This applies to any ordinary conduit (circular con duit not flowing full, oval, square, or rectangular) but not to extremely narrow shapes such as Etnnular or elongated openings, where width is small relative to length. In such cases, the hydraulic radius is approximately equal to the width of the passage. i Velocity and pressure drop calculations are based on actual flow area.) CRANE CHAPTER l -THEORY Of HOW IN PIPE 1-5 General Energy Equation Bernoulli's Theorem The Bernoulli theorem is a means of expressing the application of the law of conservation of energy to the flow of fluids in a conduit. The total energy at any particular point, above some arbitrary horizontal datum plane, is equal to the sum of the elevation head, the pressure head, and the velocity head, as follows: z + I4 + 11 H P 2g If friction losses are neglected and no energy is added to, or taken from, a piping system (i.e., pumps or turbines), the total head, H, in the above equation will be a constant for any point in the fluid. How ever, in actual practice, losses or energy increases or decreases are encountered and must be included in the Bernoulli equation. Thus, an energy balance may be written for two points in a fluid, as shown in the example in Figure 1-4. Flgur* 1-4 Energy Balance for Two Polntt in a Fluid By permission, from Fluid Mechanics1* by R. A. Dodge and M. J. Thompson. Copyright 1937; McGraw-Hill Book Company, Inc. Note the pipe friction loss from point 1 to point 2 is hL foot pounds per pound of flowing fluid; this is sometimes referred to as the head loss in feet of fluid. The equation may be written as follows: 144P1 , Zi + r? _ Z^l +, _144_Pt Equation 1-3 + h& All practical formulas for the flow of fluids are de rived from Bernoulli's theorem, wi' h modifications to account for losses due to friction. Measurement of Pressure Any Pressure Above Atmospheric At Atmospheric Pressure Level--Variable + T Any Pressure Below Atmospheric Figure 1-5 graphically illustrates the relationship between gauge and absolute pressures. Perfect vacuum cannot exist on the surface of the earth, but it nevertheless makes a convenient datum for the measurement of pressure. Barometric pressure is the level of the atmospheric pressure above perfect vacuum. "Standard" atmospheric pressure is 14.696 pounds per square inch, or 760 millimeters of mercury. Absolute Zero of Pressure--Perfect Vacuum Flgur* 1-5 Relationship Botwoon Gaug* and Absolut* Prsssurss Gauge pressure is measured above atmospheric pres sure, while absolute pressure always refers to perfect vacuum as a base. Vacuum, usually expressed in inches of mercury, is. the depression of pressure below the atmospheric level. Reference to vacuum conditions is often made by expressing the absolute pressure in inches of mercury; also millimeters of mercury and microns of mercury. *AII euporiar ftguros utod as reference marks refer to the Bibliography; too pag* C-1. age-r | i 1-6 i CHAPTER 1 - THEORY OF FlOW IN PIPE Darcy's Formula General Equation for Flow of Fluids CRANE b u m aaaaa Flow in pipe is always accompanied by friction of has lower limits based on laminar flow and upper fluid particles rubbing against one another, and con limits based on turbulent flow conditions. sequently, by loss of energy available for work; in other words, there must be a pressure drop in the At Reynolds numbers above approximately 4000, direction of flow. If ordinary Bourdon tube pressure flow conditions again become more stable and definite gauges were connected to a pipe containing a flowing friction factors can be established. This is impor fluid, as shown in Fig- . ure 1-6, gauge Pi P\ <S|L|p)fV tant because it enables the engineer to determine the flow characteristics of any fluid flowing in a would indicate a j;---C ~ ; pipe, providing the viscosity and weight density at higher static pressure 0 " 3 flowing conditions are known. For this reason, Equa f than gauge Pj. eigun i-6 tion 1-4 is recommended in preference to some of the commonly known empirical equations for the \ The general equation for pressure drop, known as flow of water, oil, and other liquids, as well as for Darcy's formula and expressed in feet of fluid, is the flow of compressible fluids when restrictions hL = fLvz/D 2g. This equation may be written to previously mentioned are observed. express .pressure drop in pounds per square inch, by substitution of proper units, as follows: If the flow is laminar (R, < 2000), the friction fac tor may be determined from the equation: AP 144 D 2g Equation 1-4 (For other forms of this equation, see page 3-2.) f _ 64 _ 64 He _ 64 M 1 Re Dvp 124 dvp The Darcy equation is valid for laminar or turbulent flow of any liquid in a pipe. However, when extreme If this quantity is substituted into Equation 1-4, the pressure drop in pounds per square inch is : velocities occurring in a pipe cause the downstream pressure to fall to the vapor pressure of the liquid, AP = 0.000 668 equation 1-5 cavitation occurs and calculated flow rates will be inaccurate. With suitable restrictions, the Darcy which is Poiseuille's law for laminar flow. equation may be used when gases and vapors (com pressible fluids) are being handled. These restric tions are defined on page 1-7. When the flow is turbulent (Rt > 4000), the friction factor depends not only upon the Reynolds number but also upon the relative roughness, t/D ... . the Equation 1-4 gives the loss in pressure due to friction and applies to pipe of constant diameter carrying fluids of reasonably constant weight density in straight pipe, whether horizontal, vertical, or sloping. For inclined pipe, vertical pipe, or pipe of varying diameter, the change in pressure due to changes in roughness of the pipe walls (), as compared to the diameter of the pipe (D). For very smooth pipes such as drawn brass tubing and glass, the friction factor decreases more rapidly with increasing Rey nolds number than for pipe with comparatively rough walls. elevation, velocity, and weight density of the fluid must be made in accordance with Bernoulli's theorem (page 1-5). For an example using this theorem, see page 4-8. Since the character of the internal surface of com mercial pipe is practically independent of the diam eter, the roughness of the walls has a greater effect on the friction factor in the small sizes. Conse Friction factor: The Darcy formula can be ration quently, pipe of small diameter will approach the ally derived by dimensional analysis, with the excep very rough condition and, in general, will have 1 tion of the friction factor, /, which must be deter higher friction factors than large pipe of the same mined experimentally. The friction factor for lami material. nar flow conditions (Re < 2000) is a function of Reynolds number only; whereas, for turbulent flow The most useful and widely accepted data of friction A (R,, > 4000), it is also a function of the character of factors for use with the Darcy formula have been pre the pipe wall. sented by L. F. Moody18 and are reproduced on pages A region known as the "critical zone" occurs between Reynolds number of approximately 2000 and 4000. In this region, the flow may be either laminar or tur A-23 to A-25. Professor Moody improved upon the well-established Pigott and Kemler friction factor diagram, incorporating more recent investigations and developments of many outstanding scientists. bulent depending upon several factors; these include changes in section or direction of flow and obstruc The friction factor, /, is plotted on page A-24 on tions, such as valves, in the upstream piping. The the basis of relative roughness obtained from the friction factor in this region is indeterminate and chart on page A-23 and the Reynolds number. The h i ss UttOkU*. CRANE CHAWEU 1 - THfO*Y Of HOW IN Hn Darcy's Formula General Equation for Flow of Fluids -- continued 1-7 value of/ is determined by horizonta 1 projection from the intersection of the e/D curve under considera tion with the calculated Reynolds number to the left hand vertical scale of the chart on page A-23. Since most calculations involve commercial steel or wrought iron pipe, the chart on page A-25 is furnished for a more direct solution. It should be kept in mind that these figures apply to clean new pipe. Effect of age and use on pipe friction: Friction loss in pipe is sensitive to changes in diameter and roughness of pipe. For a given rate of flow and a fixed friction factor, the pressure drop per foot of pipe varies inversely- with the fifth power of the diameter. Therefore, a 2% reduction of diameter causes a 10% increase in pressure drop; a 5% reduc tion of diameter increases pressure drop 23%. In many services, the interior of pipe becomes encrusted with scale, dirt, tubercules or other foreign matter; thus, it is often prudent to make allowance for ex pected diameter changes. Authorities2 point out that roughness may be ex pected to increase with use (due to corrosion or incrustation) at a rate determined by the pipe material and nature of the fluid. Ippen18, in discuss ing the effect of aging, cites a 4-inch galvanized steel pipe which had its roughness doubled and its friction factor increased 20% after three years of moderate use. Principles of Compressible Flow in Pipe An accurate determination of the pressure drop of a compressible fluid flowing through a pipe requires a knowledge of the relationship between pressure and specific volume; this is not easily determined in each particular problem. The usual extremes con sidered are adiabatic flow (p'V\ = constant) and iso thermal flow {p'Va = constant). Adiabatic flow is usually assumed, in short, perfectly insulated pipe. This would be consistent since no heat is transferred to or from the pipe, except for the fact that the minute amount of heat generated by friction is added to the flow. Isothermal flow or flow at constant temperature is often assumed, partly for convenience but more often because it is closer to fact in piping practice. The most outstanding case-of isothermal flow occurs in natural gas pipe lines. Dodge and Thompson1 show that gas flow in insulated pipe is closely approximated by isothermal flow for reasonably high pressures. Since the relationship between pressure and volume may follow some other relationship (p'Va = con stant) called polytropic flow, specific information in each individual case is almost an impossibility. The density of gases and vapors changes considerably with changes in pressure; therefore, if the pressure drop between Pi and P2 in Figure 1-6 is great, the density and velocity will change appreciably. When dealing with compressible fluids, such as air, steam, etc., the following restrictions should be observed in applying the Darcy formula: 1. If the calculated pressure drop (Pi -- P2) is less than about 10% of the inlet pressure Pt, reason able accuracy will be obtained if the specific volume used in the formula is based upon either the upstream or downstream conditions, which ever are known. 2. If the calculated pressure drop (Pi -- P$) is greater than about 10%, but less than about 40% of inlet pressure Pi, the Darcy equation may be used with reasonable accuracy by using a specific volume based, upon the average of upstream and downstream conditions; otherwise, the method given on page i-q may be used. 1 For greater pressure drops, such as are often encountered in long pipe lines, the methods given on the next two pages should be used. (continued on th+ pagm) *aaae I 1-8 C R A N E_____________________________ ________________________ CHAPTER 1 - THEORY OF FLOW IN PIPE __________ ___________________________________ Principles of Compressible Flow in Pipe i (continued) Complete isothermal equation: The flow of gases in long pipe lines closely approximates isothermal con ditions. The pressure drop in such lines is often large relative to the inlet pressure, and solution of this problem falls outside the limitations of the Darcy equation. An accurate determination of the flow characteristics falling within this category can be made by using the complete isothermal equation: Equation i-i ' 144 g A2 " r cPi)2 - (wi w2 = _V,(+ 2logeg)_ p[ Panhandle formula3 for natural gas pipe lines 6 to 24-inch diameter, Reynolds numbers 5 x 10s to 14 x 10, and S,, = 0.6: Equation 1-9 The flow efficiency factor E is defined as an expe rience factor and is usually assumed to be 0.92 or 92% for average operating conditions. Suggested values for E for other operating conditions are given on page 3-3. im n s tts The formula is developed on the basis of these Comparison of formulas for compressible flow assumptions: in pipe lines: Equations 1-7, 1-8, and 1-9 are de i 1. Isothermal flow. 2. No mechanical work is done on or by the system. rived from the same basic formula, but differ in the selection of data used for the determination of the 3. Steady flow or discharge unchanged with time. 4. The gas obeys the perfect gas laws. friction factors. 5. The velocity may be represented by the average velocity at a cross section. 6. The friction factor is constant along the pipe. 7. The pipe line is straight and horizontal between end points. Friction factors in accordance with the Moody18 dia gram are normally used with the Simplified Com pressible Flow formula (Equation 1-7). However, if the same friction factors employed in the Weymouth or Panhandle formulas are used in the Simplified Simplified Compressible Flow--Gas Pipe Line formula, identical answers will be obtained. Formula: In the practice of gas pipe line engineer ing, another assumption is added to the foregoing: 8. Acceleration can be neglected because the pipe line is long. The Weymouth friction factor34 is defined as: , 0.032 Then, the formula for discharge in a horizontal pipe J ~ rfi/3 may be written: This is identical to the Moody friction factor in the fully turbulent flow range for 20-inch I.D. pipe only. Weymouth friction factors are greater than Moody factors for sizes less than 20-inch, and smaller for This is equivalent to the complete isothermal equa sizes larger than 20-inch. tion if the pipe line is long and also for shorter lines if the ratio of pressure drop to initial pressure is small. The Panhandle friction factor3 is defined as: Since gas flow problems are usually expressed in terms of cubic feet per hour at standard conditions, it is convenient to rewrite Equation 1-7 as follows: 9* = 114.2 (P'i)2 - (P'2) 1 d5 Equation I-7a f Lm TS, Other commonly used formulas for compress ible flow in long pipe lines: Weymouth formula24: Equation 1-8 / 0.1225 0.1461 In the flow range to which the Panhandle formula is limited, this results in friction factors that are lower than those obtained from either the Moody data or the Weymouth friction formula. As a result, flow rates obtained by solution of the Panhandle formula are usually greater than those obtained by employing either the Simplified Compressible Flow formula with Moody friction factors, or the Weymouth formula. An example of the variation in flow rates which may be obtained for a specific condition by employing these formulas is given on page 4-11. WM CRANE CHAPTER I - THEORY OF F10W IN FIFE Principles of Compressible Flow in Pipe (continued) T-V Limiting flow of gases and vapors: The feature not evident in the preceding formulas (Equations 1-4 and 1-6 to 1-9 inclusive) is that the weight rate of flow (e.g., lbs/sec) of a compressible fluid in a pipe, with a given upstream pressure, will approach a cer tain maximum rate which it cannot exceed, no mat ter how much the downstream pressure is further reduced. The maximum velocity of a compressible fluid in pipe is limited by the velocity of propagation of a pres sure wave which travels at the speed of sound in the fluid. Since pressure falls off and velocity in creases as fluid proceeds downstream in pipe of uni form cross section, the maximum velocity occurs in the downstream end of the pipe. If the pressure drop is sufficiently high, the exit velocity will reach the velocity of sound. Further decrease in the out let pressure will not be felt upstream because the pressure wave can only travel at sonic velocity, and the "signal" will never translate upstream. The "surplus" pressure drop obtained by lowering the outlet pressure after the maximum discharge has already been reached takes place beyond the end of the pipe. This pressure is lost in shock waves and turbulence of the jetting fluid. The maximum possible velocity in the pipe is sonic velocity, which is expressed as: Equation 1-10 v, = V kg RT = V kg 144 P' V The value of k, the ratio of specific heats at con stant pressure to constant volume, is 1.4 for most diatomic gases; see pages A-8 and A-9 for values of k for gases and steam respectively. This velocity will occur at the outlet end or in a constricted area,when the pressure drop is sufficiently high. The pressure, temperature, and specific volume are those occurring at the point in question. When com pressible fluids discharge from the end of a reasonably short pipe of uniform cross section into an area of larger cross section, the flow is usually considered to be adiabatic. This assumption is supported by ex perimental data on pipe having lengths of 220 and 130 pipe diameters discharging air to atmosphere. Investigation of the complete theoretical analysis of adiabatic flow19 has led to a basis for establishing correction factors, which may be applied to the 'Darcy equation for this condition of flow. Since these correction factors compensate for the changes in fluid properties due to expansion of the fluid, they are identified as Y net expansion factors; see page A-22. The Darcy formula, including the Y factor, is: W = O.525 Yd?yJ-j^r Equation MI (Resistance coefficient K is defined on page 2-8) It should be noted that the value of K in this equa tion is the total resistance coefficient of the pipe line, including entrance and exit losses when they exist, and losses due to valves and fittings. The pressure drop, AP, in the ratio AP/P\ which is used for the determination of Y from the charts on page A-22, is the measured difference between the inlet pressure and the pressure in the area of larger cross section. In a system discharging compressible fluids to atmosphere, this AP is equal to the inlet gauge pressure, or the difference between absolute inlet pressure and atmospheric pressure. This value of AP is also used in Equation 1-11, whenever the Y factor falls within the limits defined by the re sistance factor K curves in the charts on page A-22. When the ratio of AP/P\, using AP as defined above, falls beyond the limits of the K curves in the charts, sonic velocity occurs at the point of discharg ' or at some restriction within the pipe, and the limit ing values for Y and AP, as determined from the tabulations to the right of the charts on page A-22, must be used in Equation 1-11. Application of Equation 1-11 and the determination of values for K, Y, and AP in the formula is demon strated in examples on pages 4-13 and 4-14. The charts on page A-22 are based upon the general gas laws for perfect gases and, at sonic velocity conditions at the outlet end, will yield accurate results for all gases which approximately follow the perfect gas laws. Steam and vapors deviate from the perfect gas laws, and application of the Y factor obtained from the charts to these flows, will there fore yield flow rates slightly greater (up to about 5%) than those calculated on the basis of sonic velocity at the outlet. However, greater accuracy will be obtained if the charts are used to establish the downstream pressure when sonic velocity occurs, and the fluid properties at this pressure condition are used in the sonic velocity and continuity equa tions (Equations 3-8 and 3-2 respectively) to de termine the flow rate. An example of this type of flow problem is presented on page 4-13. This condition of flow is comparable to the flow through nozzles and venturi tubes, covered <pn page 2-15, and the solutions of such problems are similar. --* IH -ISSffffggfflIBBBBaB frH I H i l t / 1-10 i CHAPTER 1 - THEORY OF FlOW IN PIPE Steam General Discussion CRANE Substances exist in any one of three phases .... solid, liquid, or gas. When outside conditions are varied, they may change from one phase to another. Water under normal atmospheric conditions exists in the form of a liquid. When a body of water is heated by means of some external medium, the' tem perature of the water rises and soon small bubbles, which break and form continuously, are noted on the surface. This phenomenon is described as "boiling". change the liquid into a vapor at atmospheric pres sure (14.7 psia), 970.3 Btu must be added to each pound of water after the temperature of 212 F is reached. During this transition period, the tem perature remains constant. The added quantity of heat is called the latent heat of evaporation. Conse quently, the total heat of the vapor, formed when water boils at atmospheric pressure, is the sum of the two quantities .... 180.1 Btu and 970.3 Btu, or, 1150.4 Btu per pound. The amount of heat necessary to cause the tempera ture of the water to rise is expressed in British Ther mal Units (Btu), where, 1 Btu is the quantity of heat required to raise the temperature of one pound of water from 60 to 61 F. The amount of heat neces sary to raise the temperature of a pound of water from 32 F (freezing point) to 212 F (boiling point) is 180.1 Btu. When the pressure does not exceed 50 pounds per square inch absolute, it is usually per missible to assume that each temperature increase of 1 F represents a heat content increase of one Btu per pound, regardless of the temperature of the water. Assuming the generally accepted reference plane for zero heat content at 32' F, one pound of water at 212 F contains 180.1 Btu. This quantity of heat is called heat of the liquid or sensible heat. In order to If water is heated in a closed vessel not completely filled, the pressure will rise after steam begins to form accompanied by an increase in temperature. Saturated steam is steam in contact with liquid water from which it was generated, at a tempera ture which is the boiling point of the water and the condensing point of the steam. It may be either "dry" or "wet", depending on the generating con ditions. "Dry" saturated steam is steam free from mechanically mixed water particles. "Wet satu rated steam, on the other hand, contains water particles in suspension. Saturated steam at any pressure has a definite temperature. Superheated sfeom is steam at any given pressure which is heated to a temperature higher than the temperature of saturated steam at that pressure. Flow of Fluids Through Valves and Fittings 2-1 CHAPTER 2 The preceding chapter has been devoted to- the theory and formulas used in the study of fluid flow in pipes. Since industrial installations usually con tain a considerable number of valves and fittings, a knowledge of their resistance to the flow of fluids is necessary to determine the flow characteristics of a complete piping system. Many texts on hydraulics contain no information on the resistance of valves and fittings to flow, while others present only a limited discussion of the sub ject. In realization of the need for more complete detailed information on the resistance of valves and fittings to flow, Crane Co. has conducted extensive tests in their Engineering Laboratories and has also sponsored investigations in other laboratories. These tests have been supplemented by a thorough study of all published data on this subject. Appendix A contains data from these many separate tests and the findings have been combined to furnish a basis for calculating the pressure drop through valves and fittings. Representative resistances to flow of various types of piping components are given on pages A-26, A-27, and A-30. For conversion of "equivalent length in pipe diameters", as obtained from page A-27 or A-30, to "equivalent length in feet of pipe" for any size of valve.or fitting, see page A-31. The chart on page A-31 also illustrates the correlation of equivalent length, resistance coefficient K, and pipe size. A chart is presented on page A-32 which may be used to readily determine the Cv flow coefficient of any valve for which the resistance coefficient is known or can be determined from page A-30 and page A-31. A discussion of the equivalent length and resistance coefficient K, as well as the flow coefficient Cv meth ods of calculating pressure drop through valves and fittings is presented on pages 2-8 and 2-9. / 2-2 CHAPTER 2 -- FLOW OF FLUIDS THROUGH VALVES AND FITTINGS Types of Valves and Fittings Used in Pipe Systems CRANE Valves: Although the great variety of valve designs precludes any thorough classification, most of the designs may be considered as modifications of the two basic types: Fittings: Fittings may be classified as branching, reducing, expanding, or deflecting, Such fittings as tees, crosses, side outlet elbows, etc., may be called branching fittings. 1. the gate type 2. the globe type If valves were classified according to the resistance which they offer to flow, the gate type valves would be put in the low resistance class and the globe type valves in the high resistance class. The classi fication is not all-inclusive, however, because a large number of modified valve types fall between the two extremes. Some of the most-commonly used valve designs are illustrated on pages A-28 and A-29. Reducing or expanding fittings are those which change the area of the fluid passageway. In this class are reducers and bushings. Deflecting fittings .... bends, elbows, return bends, etc........ are those which change the direction of flow. Some fittings, of course, may be combinations of ahy of the foregoing general classifications. In addi tion, there are types such as couplings and unions which offer no appreciable resistance to flow and, therefore, need not be considered here. vwv>. .11. --------- - Pressure Drop Chargeable To Valves and Fittings When a fluid is flowing steadily in a long straight pipe of uniform diameter, the flow pattern, as indi cated by the velocity distribution across the pipe diameter, will assume a certain characteristic form. Any impediment in the pipe which changes the direc tion of the whole stream, or even part of it, will alter the characteristic flow pattern and-create tur bulence, causing an energy loss greater than that normally accompanying flow in straight pipe. Be cause valves and fittings in a pipe line disturb the flow pattern, they produce an additional pressure drop. The loss of pressure produced by a valve (or fitting) consists of: 1. The pressure drop within the valve itself. 2. The pressure drop in the upstream piping in excess of that which would normally occur if there were no valve in the line. This effect is small. 3. The pressure drop in the downstream piping in excess of that which would normally occur if there were no valve in the line. This effect may be comparatively large. From the experimental point of view it is difficult to measure the three items separately. Their combined effect is the desired quantity, however, and this can be accurately measured by well known methods. Figure 2-1 Figure 2-1 shows two sections of a pipe line of the same diameter and length. The upper section con tains a globe valve. If the pressure drops, APi and APi, were measured between the points indicated, it would be found that APi is greater than AP2. Actually the loss chargeable to a valve of length "d" is APi minus the loss in a section of pipe of length "a + b' The losses, expressed in terms of equiva lent length in pipe diameters, of various valves,and fittings as given on page A-30, include the loss due to the length of the valve or fitting. CHAPTER 2 - FlOW OF FLUIDS THROUGH VAIVK AND FITTINGS Crane Flow Tests ,n Crane Engineering Laboratories have facili ties for conducting water, steam, and air flow tests for many sizes and types of valves and fittings. Although a de tailed discussion of all the various tests performed is beyond the scope of this paper, a brief description of some of the apparatus will be of interest. The test piping shown in Figure 2-3 is unique in that 6-inch gate, globe, and angle valves or 90 degree ells and tees can be tested with either water or steam. The vertical leg of the angle test section permits testing of angle lift check and stop check valves. Saturated steam at 150 psi is available at flow rates up to 100,000 pounds per hour. The steam is throt tled to the desired pressure and its state is deter mined at the meter as well as upstream and down stream from the test specimen. Figure 2-2 Flow tat piping for 12-tfch oost <tool ongio rah* For tests on water, a steam turbine driven pump sup plies water at rates up to 1200 gallons per minute through the test piping. Static pressure differential is measured by means of a manometer connected to piezometer rings upstream and downstream from test position 1 in the angle test section, or test position 2 in the straight test sec tion. The downstream piezometer for the angle test section serves as the upstream piezometer for the straight test section. Measured pressure drop for the pipe alone between piezometer stations is subtracted f 3m the pressure drop through the valve plus pipe to ascertain the pressure drop chargeable to the valve alone. Results of some of the flow tests conducted in the Crane Engineering Laboratories are plotted in Fig ures 2-4 to 2-7 shown on the two pages following. H-H .ft* 2-4 CHAPTER 2-FLOW OF FLUIDS THROUGH VALVES AND FITTINGS Crane Water Flow Tests CRANE I i i.iWwIihaH tMUMhl tWtft mmi EHt m 18tt Figur* 2-5 Water Flow Tests -- Curves 1 to 18 i Fluid Figure No. Curve No. Size, Inches 1 3/ 22 3 4. 46 Valve Type* 150-Pound Cast Iron Y-Pattem Globe Valve, Flat Seat Figure 2-4 5 6 7 8 m 2 2% 3 150-Pound Brass Angle Valve with Composition Disc, Flat Seat Water 9 lVz 10 2 11 2% 12 3 150-Pound Brass Conventional Globe Valve With Composition Disc--Flat Seat Figure 2-5 ' 13 14 15 16 17 18 % % 3/ 1% 2 6 200-Pound Brass Swing Check Valve 125-Pound Iron Body Swing Check Valve Except for check valves at lower velocities where curves (14 to 17) bend, all valves were tested with disc hilly lifted. CRANE CHATTER 2 -- FLOW Or FLUIDS THROUGH VALVES AND FITTINGS Crane Steam Flow Tests n 2-5 1 Figure 2-6 Figure 2-7 Fluid Figure Curve No. 19 20 21 22 Steam Flow Tests -- Curves 19 to 31 Size, Inches . Valve* or Fitting Type 2 300-Pound Brass Conventional Globe Valve....................... Plug Type Seat 6 300-Pound Steel Conventional Globe Valve........................ Plug Type Seat 6 300-Pound Steel Angle Valve................................................... Plug Type Seat 6 300-Pound Steel Angle Valve............................................... Ball to Cone Seat Saturated 50 psi gauge Figure 2-7 23 24 25 . 26 27 28 29 30 31 6 600-Pound Steel Angle Stop-Check Valve 6 600-Pound Steel Y-Pattem Globe Stop-Check Valve 6 600-Pound Steel Angle Valve 6 600-Pound Steel Y-Pattem Globe Valve 2 90 Short Radius Elbow for Use with Schedule 40 Pipe 6 250-Pound Cast Iron Flanged Conventional 90 Elbow 6 600-Pound Steel Gate Valve 6 125-Pound Cast Iron Gate Valve . 6 150-Pound Steel Gate Valve Except for check valves at lower velocities where curves (23 and 24) bend, all valves were tested with disc fully lifted. 2-6 CHAPTER 2 - PlOW OP FlUIDS THROUGH VALVES AND FITTINGS CRANE 1 mm i Figure 2-9 Steam capacity tef of a '/finch bran relief valve. _T_ m aw Flgyrt 2-10 Flow test piping for 2'ineh fabricated steel y-pattem globe valve. I CRANE . chafte* 2- now of fluids thuough valves and fittings 2-7 Relationship of Pressure Drop to Velocity of Flow Many experiments have shown that the head loss due to valves and fittings is proportional to a constant power of the velocity. When pressure drop or head loss is plotted against velocity on logarithmic co ordinates, the resulting curve is therefore a straight line. In the turbulent flow range, the value of the exponent of v has been found to vary from about 1.8 to 2.1 for different designs of valves and fittings. However, for all practical purposes, it can be as sumed that the pressure drop or head loss due to the flow of fluids in the turbulent range through valves and fittings varies as the square of the velocity. This relationship of pressure drop to velocity of flow is valid for check valves, only if there is suffi cient flow to hold the disc in a wide open position. The point of deviation of the test curves from a straight line, as illustrated in Figures 2-5 and 2-6, defines the flow conditions necessary to support a check valve disc in the wide open position. Most of the difficulties encountered with'check valves, both lift and swing types, have been found to be due to oversizing which results in noisy operation and premature wear of the moving parts. Referring again to Figure 2-6, it will be noted that the pressure drop, at the point where the two curves representing check valves deviate from a straight line, is about 1to 2 pounds per square inch. This value will vary somewhat for different valve designs depending upon the relative weight and size of the disc; however, it has been found to be a good "rule of thumb" to size check valves so that the pressure drop in the fully open position is about 2 psi in lift checks and about Yi psi in swing checks. This rule applies only to check valves designed on the basis of estab lished fundamental considerations which assure a full disc lift at low flow rates. On some poorly designed lift check valves, tests have shown that the disc will not lift fully even at extremely high flow rates. In many cases, application of this rule will result in check valves smaller in size than the pipe line; however, the actual pressure drop will be little, if any, higher than that of a full size valve which is used in other than a wide open position. The losses due to sudden contraction and enlarge ment which will occur in such an installation with bushings or reducing flanges can be readily calculated from the data given on page A-26. If tapered reduc ers are used, the loss due to gradual contraction at the inlet to the smaller size valve is partially com pensated for by the corresponding gradual enlarge ment on the outlet side, so that the added pressure drop due to these effects is minor. In-line ball check valves of the design shown in Figure 2-11 should be in stalled in a horizontal posi tion wherever possible. In this position, the flow re quired to move the disc, to the fully open position is very low and the valves can be full size to match the pipe line; this will result in low pressure drop Figure 2-11 In-line ball check valve In horizontal position at all flow rates. If it is necessary to install this type of valve in a vertical line, due to piping arrange ment or for other reasons, it should be sized so that the flow rate will be sufficient to cause a pressure drop of about 2J^ psi across the valve. This will provide full disc lift and prevent noisy operation and premature wear of parts. . m m m m nm m m m s 2-8 CHAPTER 2-FLOW OF FLUIDS THROUGH VALVES AND FITTINGS CRANE Resistance Coefficient K, Equivalent Length L/D, . And Flow Coefficient Cv The numerous types of valves and fittings and the great variety of service conditions make it virtually impossible to obtain test data on every size and type of valve and fitting used today. For this reason, it is desirable to find a means for utilizing the limited test data which are available. Severa' methods of accomplishing this have been devised; the most commonly used are the "equivalent length", "resistancecoefficient", and "flowcoefficient". Velocity in a pipe is obtained at the expense of static head, and decrease in static head due to velocity is: h = --> U Equation 2-1 ' which is defined as the "velocity head". Flow through a valve or fitting in a pipe line also causes a reduction in static head which may be expressed in terms of velocity head. The resistance coefficient K in the equation similarity is shown in Figure 2-13 where a 12-inch standard elbow has been drawn to 1/6 scale of a 2-inch standard elbow, so that their port diameters are iden tical. The flow paths through the two fittings drawn to these scales would also have to be identical to have geometric similarity; in addition, the relative roughness of the surfaces would have to be similar. Figure 2-14 on the opposite page is based on the analysis of extensive test data from various sources. The K coefficients for a number of lines of valves and fittings have been plotted against size. It will be noted that the slopes of the K curves show a definite tendency to follow the same slope as the /(L/D) curve for straight pipe. It is probably coin cidence that the effect of geometric dissimilarity between different sizes of the same line of valves or fittings upon the resistance coefficient K is similar to that of relative roughness, or size of pipe, upon friction factor. Equation 2-2 therefore, is defined as the number of velocity heads lost due to the valve or fitting. Also, the same head loss in straight pipe is expressed by the Darcy equation Equation 2-3 It follows that, - H) Equation 2-4 The ratio L/D is the equivalent length in pipe diam eters of straight pipe which will cause the same pressure drop as the valve under the same flow conditions. The resistance co efficient K would theoretically be a constant for all sizes of a given design or line of valves and fittings if all sizes were geometrically similar. However, geometric similarity is seldom, if ever, achieved because Figur* 2-13 the design of valves Geometrical dissimilarity between 2 and and fittings is dic 12-inch standard cast iron flanged elbows tated by manufac turing economies, standards, structural strength, and other considerations. An example of geometric dis Based on the evidence presented in Figure 2-14, it can be said that the resistance coefficient K, for a given line of valves or fittings, tends to vary with size as does the friction factor / for straight pipe, and that the equivalent length L/D tends toward a con stant for the various sizes of a given line of valves or fittings. In the flow range of complete turbulence as defined by the Friction Factor Charts, pages A-24 and A-25, the K coefficient for a given size and the L/D value are, of course, constant. In the transition zone, where / for pipe increases with decreasing Reynolds numbers, it is assumed that the value of L/D is con stant and that K varies in the same manner as the friction factor. Limited tests have shown that this is not an exact relationship and that it may vary for different types of valves and fittings; however, since the tendency is in this direction, it is believed to provide more accurate solutions than would the assumption that K is constant for all Reynolds numbers. It has been found convenient in some branches of the valve industry, particularly in connection with con trol valves, to express the valve capacity and the valve flow characteristics in terms of the flow coeffi cient Cv. The Cv coefficient of a valve is defined as the flow of water at 60 F, in gallons per minute, at a pressure drop of one pound per square 'inch across the valve. By the substitution of appropriate equivalent units in the Darcy equation, it can be shown that, Cv = 19'9^ = \If-D VK Equation 2-5 (continued on noxt pago) 9 * CRANE CHAFTE* 2 - now op huids thkough valves ano fittings Resistance Coefficient K, Equivalent Length l/D, And Flow Coefficient Cv -- continued 2-9" Symbol O o- 9 -o 6 -o- cf Figure 2-14, Variation of Resistance Coefficient K ( =f L/D) with Size Product Tested Authority Schedule 40 Pipe, 30 Diameters Long (K = 30 f)....... .Moody A.S.M.E. Trans., Nov.-1944` 125-Pound Iron Body Wedge Gate Valves........................ Univ. of Wise. Exp. Sta. Bull., Vol. 9, No. 1, 19221* 600-Pound Steel Wedge Gate Valves.................................. Crane Tests 90 Degree Pipe Bends, R/D = 2...........................................Pigott A.S.M.E. 90 Degree Pipe Bends, R/D = 3...........................................Pigott A.S.M.E. 90 Degree Pipe Bends, R/D 1...........................................Pigott A.S.M.E. Trans., 1950* Trans., 19J0* Trans., 1950* ' 600-Pound Steel Wedge Gate Valves, Seat Reduced... .Crane Tests 300-Pound Steel Venturi Ball-Cage Gate Valves.............Crane-Armour Tests 125-Pound Iron Body Y-Pattem Globe Valves................ Crane-Armour Tests 125-Pound Brass Angle Valves, Composition Disc........ Crane Tests 125-Pound Brass Globe Valves, Composition Disc........ Crane Tests (continued from the preceding page). Also, the quantity in gallons per minute of any liquid having a viscosity close to that of water at 60 F that will flow through the valve can be deter mined from: . same formula arranged as follows: Equation 2-6 Q-C^AP^) Q-7-9C,yj Equation 2-6 and the pressure drop can be computed from the Since Equations 2-2, 2-3, and 2-6 are simply other forms of the Darcy equation, the limitations regard ing their use for compressible flow (explained in Chapter 1, Page 1-7) apply. Other convenient forms of Equations 2-2, 2-3, and 2-6 in terms of commonly used units are presented on page 3-4. vt*" -uo.v faitiKwiw rr i .-~ . .,. 2-10 CHAPTER 2 - Flow OF FLUIDS THROUGH VAIVES AND FITTINGS CRANE Relationship of Equivalent Length L/D and Resistance Coefficient K To Inside Diameter of Connecting Pipe Tests have shown that the pressure drop due to a given valve or fitting does not change when the product is installed with pipe of the same nominal size but of different thickness. Small variations in entrance and exit losses caused by mating the valve ends to variable pipe thicknesses, within reasonable limits, are insignificant. Since the pressure drop is a function of the square of the velocity, and velocity is a function of the square of the internal diameter, it follows that the equivalent length of a given valve or fitting, expressed in terms of the pipe to which it is connected, varies as the fourth power of the in ternal diameter of the pipe. For example, if the equivalent length of a %-inch valve is determined by test to be 100 pipe diameters of Schedule 80 pipe, its equivalent length will be 169 diameters of Sched ule 40 pipe, since the ratio of the inside diameters of the two pipes to the fourth power is 1.69. This ratio, of course, varies with the different sizes and thicknesses of pipes. The same relationship applies to the resistance coefficient K. ' Computation of pressure drop using equivalent length or K coefficient data established on the basis of this table should be made using pipe dimensions spec ified on pages B-16 to B-18; for installation condi tions not in agreement with the table, the equivalent length in pipe diameters or the K resistance coeffi cient should be multiplied by the ratio of diameters to the fourth power. 4( )*Ka = K, Equation 2-7 (i).-(i), (z)' Subscript "a" defines the resistance coefficients with reference to the internal diameter of the pipe in which the valve will be installed. Subscript "b" defines the known resistance coeffi cients and the internal diameters of the pipe for which these coefficients were established. In view of this condition, the Crane Engineering Laboratories have established the practice of making all flow tests with pipe having internal diameters normally used with the particular valve or fitting. For this purpose, pipe normally used with the various pressure classes of valves and fittings has been arbi trarily established in accordance with the table shown at the top of page A-30. This procedure of obtaining equivalent length or K coefficient data with respect to pipe of various in ternal diameters corrects a significant variable that has often been neglected in translating test data and makes possi! e a more accurate prediction of the flow characteristics of untested valves and fittings by comparison of detail dimensions and shapes with tested items. th*\ Valves with Gradually Increased Ports Various types of valves are often made with reduced seats and have uniformly tapered ports. Straightthrough valves such as gates and plug cocks, when so designed, are sometimes referred to as venturi valves. When the transition from seat size to port size is uniformly tapered with an angle, approximately 20 degrees or less with the center line, the flow char acteristics may be determined in the same manner as for valves installed with pipe having an inside diam eter other than that with which the valve was tested. Tests have shown the effect of tapered port sections upon flow characteristics is minor compared to losses across the valve seat. This applies particularly to valves having relatively high flow resistances. Equation 2-7 may be used to establish approximate resistance coefficients for reduced seat valves. Effect of End Connections Analysis of many tests indicates there is little, if any, justification for assigning different resistance coefficients to a given valve or fitting with varying types of end connections. The difference between flanged, screwed, and welding ends in this respect has been found to be insignificant. The pressure drop due to unions, couplings, and flanged joints is, likewise, insignificant. CRANE CHAPTER 2- HOW Op FLUIDS THROUGH VALVES AND FITTINGS 2-11 Laminar Flow Conditions One of the problems in flow of fluids confronting engineers from time to time, for which there is very meager information, is the resistance of valves and fittings under laminar flow conditions. Flow through straight pipe is adequately covered by the basic flow equation, (n)f" w(h), *,**on** Subscript s refers to the equivalent length in pipe diameters under laminar flow conditions where the Reynolds number is less than 1000. which is identical to Poiseuille's law for laminar flow when the equation for / in this flow range, / = 64/R,, is included in the formula. Subscript refers to the equivalent length in pipe diameters determined from tests in the tur bulent flow range. Representative values of equivalent length are given in the table on page A-30. F For solution of these problems, we have developed on the basis of data presented in "Principles of Chemical Engineering" by Walker, Lewis, McAdams and Gilliland24, the empirical relationship between equivalent length in the laminar flow region to that in the turbulent region, namely: The minimum equivalent length is the length in pipe diameters of the centerline of the actual flow path through the valve or fitting. While laboratory test data supporting this method is meager, reports of field experience indicate that the results obtained agree closely with observed conditions. " Basis for Design of Charts for Determining Equivalent Length, Resistance Coefficient, and Flow Coefficient The table on page A-30 lists average equivalent length datt' expressed in pipe diameters abstracted from all available tests. It is not practical to identify all valve and fitting types with the many variations in design which may affect the flow char acteristics. The data- given for globe and angle valves represent actual tests on the variation of designs indicated. By using the data given in this table along with the principles presented from page 2-8 to this point as a basis, reasonable equivalent length values can be'estimated for any valve or fitting upon consideration of design features, such as, the relative area of seat or restricted sections to pipe diameter and the shape of the flow passage. The chart on page A-31 provides a convenient means of translating equivalent length in pipe diameters as given in the table on page A-30, to equivalent length in feet of, pipe for any given size of valve or fitting. Alsci the resistance coefficient K can be readily determined from this chart for any size, if the resistance coefficient or equivalent length for any other size of the same item has been estab lished, either by experiment or estimate. The chart on page A-3 2 gives a graphical solution of Equation 2-5 and permits a ready determination of Cv if K is known. An example- illustrating the use of this chart is given on page 4-2. Limitations of charts: As explained on page 2-8 and at the top of this page, the value of L/D for a given type of valve or fitting is considered to be constant for flow conditions resulting in Reynolds numbers of 1000 or greater. Equivalent lengths either in pipe diameters or feet of pipe, as determined from pages A-30 or A-31, are therefore legitimate for all flow conditions except in the laminar flow range where the Reynolds number is less than 1000. For Reynolds numbers less than 1000, values of L/D must be determined in accordance with Equation 2-8. On the other hand, values of K, as determined from pages A-31 and A-32, are legitimate only for flow conditions resulting in Reynolds numbers falling in the completely turbulent flow range, as defined by the friction factor on pages A-24 and A-25. At lower flow rates, values of K vary in approximately the same manner as does the value of friction factor with Reynolds number. At the lower flow rates, the value of K as determined from pages A-31 and A-32 should be multiplied by the ratio: / (at calculated Reynolds number) / (in range of complete turbulence, where / is constant) When K has been corrected for flow in the transition or laminar flow range, Cv can be obtained directly from page A-32 by employing the corrected K factor. However, if the Cv factor is furnished for the com pletely turbulent flow range, as defined by the friction factor charts on pages A-24 and A-25, it must be corrected by multiplying it by the ratio, / (in range of complete turbulence, where / is constant) / (at calculated Reynolds number) since Cv varies inversely with the square root of the friction factor. - ' / 2-12 i i\5 CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS Resistance of Bends CRANE *< Figure 2-15 Secondary Flew in Bends I Secondary flow: The nature of the flow of liquids The relationship between Kb and r/d (relative in bends has been thoroughly investigated and many radius*) is not well defined, as can be observed by interesting facts have been discovered. For example, reference to Figure 2-16 (taken from the work of when a fluid passes around a bend in either viscous Beij21). The curves in this chart indicate that Kb or turbulent flow, there is established in the bend has a minimum value when r/d is between 3 and 5. a condition known as "secondary flow". This is rotating motion, at right angles to the pipe axis, The chart on page A-27 shows the resistance of 90 which is superimposed upon the main motion in the degree bends in terms of equivalent length of straight direction of the axis. The frictional resistance of the pipe. These curves .... also based on the work of pipe walls and the action of centrifugal force com Beij .... are believed to represent average condi '! bine to produce this rotation. Figure 2-15 illus tions for the flow of fluids in 90 degree bends. trates this phenomenon. ! iI Tests have shown that the loss due to continuous Resistance of bend, to flow: The resistance or bends greater than 90 degrees, such as in pipe coils, head loss in a bend is conventionally assumed to con is less than the summation of the losses in the 90 sist of .... (1) the loss due to curvature .... (2) the degree bends contained in the coil, considered sepa excess loss in the downstream tangent.... and (3) rately. This is reasonable, since the loss hv in Equa the loss due to length, thus: tion 2-9 occurs only once in such a bend. Reason h, = hr + hc + hi Equation 2-9 where: h, = K= hc hL total loss, in feet of fluid excess loss in downstream tangent, in feet of fluid loss due to curvature, in feet of fluid loss in bend due to length, in feet of fluid ably accurate results for pipe coils and expansion loops consisting of continuous bends can be obtained by the use of the chart on page A-27 .... if the num ber of 90 degree bends contained in the coil minus one, multiplied by the resistance due to length plus one-half of the bend resistance, is added to the total resistance of a 90 degree bend. if: hb hp -f* hc then: h, -- hb + hi Equation 2-10 For example, a pipe coil consisting of four complete turns .... sixteen 90 degree bends .... and having a relative radius of five pipe diameters, would have a total equivalent length, in pipe diameters, of: 15 (8 + 4) + 16 = 196 However, the quantity hb can be expressed as a func It will be noted that this assumes hp = hc in Equa tion of velocity head in the formula: tion 2-9; this relationship has not been established j hb = K, U Equation 2-11 by tests but is believed to represent the most ac curate estimate that can be made until further experimental data are available. I where: I Kb = the bend coefficient Resistance of miter bends: The equivalent length v = velocity through pipe, feet per second of miter bends, based on the work of H. Kirchbach4, g -- 32.2 feet per second per second is also sho* n on page A-27. *The relative radius of a bend is the ratio of the mJiu, of the bend axis to the internal diameter of the pipe.-Both dimensions must be in the same units . CRANE CHAPTER 2-HOW OP PlUIDS THROUGH VALVES ANEX FITTINGS Resistance of Bends -- continued 2-13" * *o a>.3 a O "COaaQ3 'Lo \ iL \ /\ 1 --- im i A N"vO*---------- 10 12 14 16 18 20 22 Relative Radius, r/d Figure 2-16, Bend Coefficients Found by Various Investigators (Beij21) From "Pressure Losses for Fluid Flow in 90 Pipe Bends" by K. H. Beif. , Courtesy of Journal of Research of National Bureau of Standards* Investigator Diameter Symbol Balch......................... ....................... 3-inch....................... .... Davis......................... .... Brightmore............... .... Brightmore.............. ....................... 4-inch....................... .... Hofmann................. ............1.7-inch (rough pipe).......... ----- Hofmann................. ..........1.7-inch (smooth pipe) .... .... Vogel......................... ................6, 8, and 10-inch............ ----- Beij........................'.. .... O A T Other Resistances to Flow In addition to the resistance due to valves and fit tings already discussed, losses due to sudden enlarge ment and sudden contraction are encountered when ever fittings such as reducing or increasing flanges, bushings, etc., are used. Also, when a fluid enters or leaves an open end pipe, entrance and exit losses occur. As in the case of valves and fittings, these losses can be expressed by the formula: hL = K -- n Unlike most other fittings, there is no length involved in losses due to these conditions; thus, relative rough ness is not a factor in these resistances, and geometric similarity does exist. The resistance due to sudden enlargement and sudden contraction, as well as en trance and exit losses expressed in terms of velocity head or K factor, are therefore independent of pipe size. Resistance coefficient K for such conditions are given on page A-26. Equivalent lengths corresponding to these resistance coefficients for any size can be readily determined from the chart on page A-31. For example, the equiv alent lengths of sharp edged entrances (K = 0.5) to 2 and 6-inch pipes can be read from the nomograph on page A-31 as 26 diameters of 2-inch pipe and 33 diameters of 6-inch pipe, respectively. 1 / 2-14 CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS Flow Through Nozzles and Orifices The discharge of fluids through nozzles and orifices has been subject to continued investigation and, as a result, well-established data are still being supplemented. A portion of the subject is covered on these facing pages but more complete references will be found in the Bib liography8' > I0, or from the data supplied by meter manufacturers. CRANE lit* iimii--i i . fcl fctufi M m im m u m m iiin iiB ! ' The rate of flow of any fluid through an orifice or ing a low viscosity, i.e., water,, gasoline, etc., the i nozzle, neglecting the velocity of approach, may be Reynolds number need not be calculated since it expressed by: ^ will fall in the range of the values on page A-19, q = Ctf A V Xg hL equation 2-12 where the flow coefficient C is a constant. Flow of gases and vapors: The flow of compres Velocity of approach may have considerable effect on sible fluids through nozzles and orifices can be ex i the quantity discharged through a nozzle or orifice, pressed by the same equation used for liquids except j The factor correcting for velocity of approach, the net expansion factor V must be included. V - (*)` may be incorporated in Equation 2-12 as follows: qA _____ q=-- d V 2-g hi V - (*)* equation 2-13 The quantity is defined as the flow coefficient C. Values of C for nozzles and orifices are shown on page A-19. Use of the flow coefficient C eliminates the necessity for calculating the velocity of approach, and Equation 2-13 may now be written: Equation 2-14 - c A VITST - C a Orifices and nozzles are normally used in piping sys tems as metering devices and are installed with flange taps or pipe taps in' accordance with ASME specifications. The values of hL and AP in Equation 2-14 are the measured differential static head or pressure across flange taps when values of C are taken from page A-19. The flow coefficient C is plotted for Reynolds numbers based on the internal diameter of the upstream pipe. Flow of liquids: For nozzles and orifices discharg ing incompressible fluids to atmosphere, C values may be taken from page A-19 if hi or AP in Equa tion 2-14 is taken as the upstream head or gauge pressure. For most conditions of flow of fluids hav q = YCA^J28 (`4^ AP equation 2-1S The expansion factor Y is a function of: 1. The specific heat ratio, k. 2. The ratio of orifice or throat diameter to inlet diameter. 3. Ratio of downstream to upstream absolute pressures. This factor9-10 has been experimentally determined on the basis of air, which has a specific heat ratio of 1.4, and steam having specific heat ratios of approx imately 1.3, The data is plotted on page A-20 and values of other specific heat ratios have been included to extend the use of the data. Values of k for some of the common vapors and gases are given on pages A-8 and A-9. The specific heat ratio, k, may vary slightly for different pressures and temperatures, but for most practical problems the values given will provide reasonably accurate results. Equation 2-15 may be used for orifices discharging compressible fluids to atmosphere by using: 1. Flow coefficient C given on page A-19 in the Reynolds number range where C is a constant for the given diameter ratio. 2. Expansion factor Y per page A-20. 3. Differential pressure AP, equal to the inlet gauge pressure. This also applies to nozzles discharging compressible fluids to atmosphere only if the absolute inlet pres sure is less than the absolute atmospheric pressure divided by the critical pressure ratio re\ this is discussed on the next page. When the absolute inlet pressure is greater than this amount, flow through nozzles should be calculated as outlined on the following page. llO llilS S l CRANE CHAPTER 2-FlOW OF FlUIDS THROUGH VAIVES AND FITTINGS Flow Through Nozzles and Orifices -- continued 2-15 Maximum flow of compressible fluids in a noz zle: A smoothly convergent nozzle has the property of being able to deliver a compressible fluid up to the velocity of sound in its minimum cross section or throat, providing the available pressure drop is sufficiently high. Sonic velocity is the maximum velocity that may be attained in the throat of a nozzle (supersonic velocity is attained in a gradually divergent section following the convergent nozzle, when sonic velocity exists in the throat). The critical pressure ratio is the largest ratio of downstream pressure to upstream pressure capable of producing sonic velocity. Values of critical pres sure ratio re, which depend upon the ratio of nozzle diameter to upstream diameter as well as the specific heat ratio k, are given on page A-21. Flow through nozzles and venturi meters is limited by critical pressure ratio, and minimum values of Y to be used in Equation 2-15 for this condition, are indicated on page A-20 by the termination of the curves at PVP'i = re. Equation 2-15 may be used for discharge of com pressible fluids through a nozzle to atmosphere, or to a downstream pressure lower than indicated by the critical pressure ratio r,, by using values of: Y .... minimum per page A-20 C ... . page A-19 AP . . P'i (1 -- re); rc per page A-21 p .... weight density at upstream condition Flow through short tubes: Since complete experi mental data for the discharge of fluids to atmos phere through short tubes (L/D is less than, or equal to, 2.5 pipe diameters)1 are not available, it is sug gested that reasonably accurate approximations may be obtained by using Equations 2-14 and 2-15, with values of C somewhere between those for orifices and nozzles, depending upon entrance conditions. If the entrance is well rounded, C values would tend to approach those for nozzles, whereas short tubes with square entrance would have characteristics similar to those for square edged orifices. Discharge of Fluids Through Valvesf Fittings, and Pipe Liquid flow: To determine the flow of liquid through pipe, the Darcy formula is used. Equation 1-4 (page 1-6) has been converted to more convenient terms in Chapter 3 and has been rewritten as Equation 3-14. The form of Equation 3-14 which is most applicable to liquid flow is written in terms of flow rate in gallons per minute. hr. = 0.00259 KQ2 d* Loss of head in terms of resistance coefficient K has been selected since entrance and exit losses are usually given in terms of velocity head loss, K (see page A-26). Solving for Q, the equation can be rewritten. Q " V0.00259 K - `9-M2^ Q = 19.65 d2 Equation 2-16 J|v.;:. Equation 2-16 can be employed for valves, fittings, and pipe where K would be the sum of all the resist ances in the piping system, including entrance and exit losses when they exist. Examples of problems of this type are shown on page 4-12. Compressible flow: When a compressible fluid flows from a piping system into an area of larger cross sec tion than that of the pipe, as in the case of discharge to atmosphere, a modified form of the Darcy formula. Equation 1-11 developed on page 1-9, is used. Figure 2-17 Pressure meoturemenf* mad at strategic paints in a valve in order to establish optimum design. w = 0.525 Y d2 IAP \KVi The determination of values of K, Y, and AP in this equation is described on page 1-9 and is illustrated in the examples on pages 4-13 and 4-14. 2-16 i fnmn imri'iiti irfnlftaillf<rmriii CHAPTER 2 - Flow OF FLUIDS THROUGH VALVES AND FITTINGS CRANE 9 oagBsmoaiaiiHaan ! ! !1 t I \ i I i 3-! Formulas and Nomographs For Flow Through Valves, Fittings, and Pipe CHAPTER 3 Only basic formulas needed for the presentation of the theory of fluid flow through valves, fittings, and pipe were presented in the first two chapters of this paper. In the summary of formulas given in this chapter, the basic formulas are rewritten in terms of units which are most commonly used in this country. This summary provides the user with an equation which will enable him to arrive at a solution to his problem with a minimum conversion of units. Nomographs presented ,1 this chapter are graphical solutions of the flow formulas applying to pipe. Valve and fitting flow problems may also be solved by means of these nomographs by determining their equivalent length in terms of feet of straight pipe. Due to the wide variety of terms and the variation in the physical properties of liquids and gases, it was necessary to divide the nomographs into two parts: the first part (pages 3-6 to 3-15) pertains to liquid flow, and the second part (pages 3-16 to 3-25), pertains to compressible flow. All nomographs for the solution of pressure drop prob lems are based upon Darcy's formula, since it is a general formula which is applicable to all fluids and can be applied to all types of pipe through the use of the Moody Friction Factor Diagram. Darcy's form ula also provides a means of solving problems of flow through valves and fittings on the basis of equivalent length or resistance coefficient. Nomographs provide simple, rapid, practical, and reasonably accurate solu tions to flow formulas and the decimal point is accu rately located. Accuracy of a nomograph is limited by the available page space, length of scales, number of units provided on each scale, and the angle at which the connecting line crosses the scale. Whenever the solution of a problem falls beyond the range of a nomograph, the slide rule or arithmetical solution of the formula must be employed. 3-2 CHAPTER 3-FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE Summary of Formulas CRANE To eliminate needless duplication, formulas have been written in terms of either specific volume V or weight density p, but not in terms of both, since one is the reciprocal of the other. V- P1 ' V These equations may be substituted in any of the formulas shown in this paper whenever necessary. Bernoulli's theorem: Equation 3-1 Z + J44P + A = H pn 144 Pi _ cr . 144 Pi . L Zi + o pi Trg7 ~ + Pt t + "2g+ Mr, Mean velocity of flow in pipe: (Continuity Equation) Equation 3-2 v = 7T * "Jr - 0-408 v = 0.286 -Bjjj- = 1a83.3 wV d2 W = -59 u = 0.001 44 p;^ = 0.003 89 q\S, pd2 w 9m W ,W V - -X - 1-)-- - 5'06 -- V - 0.0865 ^ Reynolds number of flow in pipe: fquotien 3-3 Dvp R, = Me ---D---v-p- 7- = dvp 123.9 32.2M e M Re ~ 22700 dp _ 506 dp " 35-4 dp Rc = 6.31-^ = 0.482 ap ap RD e = --DV--v = --1-d2-vV- T = 7740 --dVv Rde = . 419000-9^ = 31,60^<3 = 394 W Viscosity equivalents: ,, = JL = Jf_ p' Equation 3-4 Head loss and pressure drop in straight pipe: Pressure loss due to flow is the same in a sloping, vertical, or horizontal pipe. However, the dif ference in pressure due to the difference in head must be considered in pressure drop calculations; see page 1-5. .' Darcy's formula: Equation 3*5 l , L i? fLii2 h^fD7i = 'l863 -- hL = bz6o^~ = 0.0311 ^ d5 h, L -- 0.015 24 /L^B2 = 0 0.000 483 f---LW-j*pV- A P = 0.001 294 /Lpv2 = 0.000 000 359 /LpV2 AP = 43.5 fLpq* d6 _= 0.000 216 /LpQ2 d6 AP = 0.000 1058 fL#pB = 0.000003 fLWV }LT{q\YSc AP = 0.000 000 007 26 d6P' fUq'tYS* AP = 0.000000019 59 d6p For simplified compressible fluid formula, see page 3*22. Head loss and pressure drop with laminar flow in straight pipe: For laminar flow conditions (Re< 2000), the friction factor is a direct mathematical function of the Reynolds number only, and can be expressed by the formula:/ = 64//?,. Substituting this value of / in the Darcy formula, it can be rewritten: pLv 0.0962 "d*P~ Equation 3-6 h, L = , 17-bS pLq d*p~ = pLQ 0.0393 --d--*-p--- h, L -- 0.0275 p^LB d<p -- 0.004 90 pd-L*--pW-2-- AP 0.000 668 pLv M^9 = 0.1225 -- ^ AP = 0.000 273 pLQ d4 == 0.000 191 pLB d4 AP = 0.000 0340 d*p ii iKMnidli 'nmnn'iw<wmwp i p>t i .ii!iii C*AM CHAPTER 3-KMMUIA8 ANDNOMOOHAPHS PO HOW THtOUOH VAIYB, FITTINGS, AND FIM5 Summary of Formulas -- continued 3-$ Limitations of Darcy formula Non-compr***lbl* flow; liquid*; The Darcy formula may be used without restriction for the flow of water, oil, and other liquids in pipe. However, when extreme velocities occurring in pipe cause the downstream pressure to fall to the vapor pressure of the liquid, cavitation occurs and cal culated flow rates are inaccurate. Compr*iibla flow; gam and vapor*: When pressure drop is less than 10% of Pi> use p or V based on either inlet or outlet conditions. When pressure drop is greater than 10% of Pi but less than 40% of Pi, use the average of p or V based on inlet and outlet conditions, or use Equa tion 3-20. When pressure drop is greater than 40% of Pi, use the rational or empirical formulas given on this page for compressible- flow, or use Equation 3-20 (for theory, see page i-q). _ Isothermal flow of gas In pipe lines Equation 3-7 Empirical formulas for the flow of water, steam, and gas Although the rational method (using Darcy's for mula) for solving flow problems has been recom mended in this paper, some engineers prefer to use empirical formulas. Hoz*n and William* Formula for flaw of wat*r; Equation 3-9 q = 0.442 d2" c (?i L p*y** where: c = 140 for new steel pipe c = 130 for new cast iron pipe c = 110 for riveted pipe Babcock formula for *t*am flow; AP = 0.000 000 0363 y AP = 0.470 Equation 3-10 J W2LV Simplified compressible flow f for long pipe lines 1 w = ., 44 gA*\ ( (P'i) - (/*,) \ q h = 1J4-2 U (P'V - (P') fUTS, \ ) & # Maximum (sonic) velocity of compressible fluids in pipe The maximum possible velocity of a compressible fluid in a pipe is equivalent to the speed of sound in the fluid; this is expressed as: V, = V k gRT Equation 3S V,.= V& g 144P' v7 68V, = .! V&P'F Spitzglass formula for low pressure gas; (proiiur* Ion than ono pound gaugo) Equation 3-TI 9 k = 3550 A K& + 003 Flowing temperature is 60 F. Weymouth formula for high prossuro ga*; 9* 28.0 '' Equation 3-12 (P'1)2 ~ (P't) S,Lm Panhandle formula1 for natural gas pip* lin** 6 fa 24-Inch diameter and I, = |J 10*) to (14 x 10*); - ,6.8E Equation 3-13 1)""" where: gas temperature = 60 F <S,, = 0.6. E = flow efficiency E = 1.00 (100%) for brand new pipe without any bends, elbows, valves, and change of pipe diameter or elevation E = 0.95 for very good operating conditions E = 0.92 for average operating conditions = 0.85 for unusually unfavorable operating conditions 3-4 CHAPTER 3-FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE Summary of Formulas -- continued CRANE Head loss and pressure drop through valves and fittings Head loss through valves and fittings is generally given in terms of resistance coefficient K which indicates static head loss through a valve in terms of "velocity head", or, equivalent length in pipe diameters L/D that will cause the same head loss as the valve. From Darcy's formula, head loss through a pipe is: Equation 3-5 and head loss through a valve is: hL = K v2 21 L therefore: K -f-v Equation 3-14 Equation 3-15 To eliminate needless duplication of formulas, the following are all given in terms of K. Whenever necessary, substitute (f L/D) for (K). hi, -- 522 Kg2 d4 _= 0.002 59 KQ* d4 Equation 3-J4 0.001 270 KB2 -gr- = 0.000 0403 xrdv< * AP -- 0.000 1078 KpiP -- 0.000 000 0300 KpV2 AADP = 3.6a2 KMPf = 0.00001799 --KpQ2 d4 d4 AP = 0.000 008 82 KpB2 d4 AP = 0.000 000 280 KFV d4 ap = 0.000000000605 K(q'/PTS' AP = 0.000000001 633 K (<A)8 cf4 p Pressure drop and flow of liquids, with viscosity similar to water at 60 F, using flow coefficient AP - (*)' P V Cv / 62.4 Equation 3*76 Q = CyyJ AP~ -7.9oCr> v^/ ApP Cv <-- 0 1 p v y V AP (62.4) ^ 891 d4 (Cv)s ,_L _ K _ 891 cf4 > / /(Cv)2 29.9 d2 V/L/D 29.9 d2 VK r _ 74.3 d* ^ - /(Cv)2 Head loss and pressure drop with laminar flow through valves; Darcy's formula hh = 0.003 28 () ~p Equation 3-17 (fc)'hL = 1.470 Jf. d3p = 0.008 02 IfjA ML AD/ dp ..h, L = 0.000 40.8/1 L \ pWV2 AP = 0.0000557 () Y = 0.010 21 Ap = 0.000 0228 ~^r ifi d* AP = 0.000 015 93 (jj) -*jr AP = 0.000 002 84 Equivalent length correction for laminar flow with R, < 1000 (*).-(& R< IOOO Equation 3-18 See pages 2-11 and A-30. Minimum (L/D), = length of center line of actual flow path through valve or fitting. Subscript s refers to equivalent length with Re < 1000. Subscript l refers to equivalent length with R, > 1000. Discharge of fluid through valves, fittings, and pipe; Darcy's formula Liquid flow: , ____ Equation 3-19 q = 0.0438 d?.yjj*r =0.525 cPyJ-j^- Q = 19.65 d2 = 236 d2 yj AP Kp w = 0.0438 d2-yj-- = 0.525 APp K W = 157.6 d2 ComprutsibU flow: = 1891 d2 ^ AP|> K VAP P' Equation 3-20 q',, - 24 700 Yd2 /' AP P, s. V K APP, K APP, K u> = 0.525 Yd2 /AP Vkv, W= 1891 Yd2 \K7, Values of Y are shown on page A-22. For K, Y, and AP determination, see examples on pages 4-13 and 4-14. CRANE CHAFTR S'- FORMULAS AND NOMOGRAFHS FOR FLOW THROUGH VALVES, FITTINGS, AND FIFE Summary of Formulas -- concluded 3-5 Flow through nozzles and orifices (hL and AP measured across flange taps) Liquid: Equation 3-2 J q - AC V 2g hL q = 0.0438 (P0 C V Q = 19.65 cPo C V hL w = 0.0438 d?0 c V hz, p2 -- 0.52.5 ^0 C VA.Pp VP = 157.6 cPo C V hL p2 ~ 1891 tfoCVAPp Values of C are shown on page A-19. Cempratiibl* fluid*: Equation 3-22 , v ,, /app7; g a = 40 700 Y cPo C-J "f j'-- g/ = 24700 --Y^=o--C V,-At-Pd-Pi K q'm = b78Yd*0C^^j^ ...... q'm = 412 VAPPi g, = 11.30vYcjP, ,,,,C ^/-A7P^P--'i g' = 6.87 V APP7 w - 0.525Y<P0C W = 1891 YcPuC^j^- Values of C are shown on page A-19. Values of Y are shown on page A-20. , Equivalents of head loss and pressure drop 144 AP h = -------------- AP Equation 3-23 ^2 P 144 Changes in resistance coefficient K and equivalent length L/D required to compensate for different pipe I. D. Equation 3-24 (too pago A-30) Subscript a refers to pipe in which valve will be installed. Subscript b refers to pipe for which the resistance coeffi cient K or the equivalent length L/D was established. Specific gravity of liquids Any liquid: Equation 3-25 5_ / any liquid at 60 F, \ p \unless otherwise specified/ P (water at 60 F) Oils: Equation 3*25 5 (6o F/6o F) i4i-5 131.5 + Deg API Liquid* lighter than water: Equation 3-27 S (bo F/6o F) 140 130 + Deg Baum^ Liquids htavitr than wafer: Equation 3-28 S (bo F/bo F) 145 145 ~ Deg Baume Specific gravity of gases ,, _ R (air) ' R (gas) 53-3 R (gas) ,, M (gas) _ M (gas) 1 M (air) . 29 Equation 3-29 General gas laws for perfect gases p'Va = waRT Equation 3-30 - E? - JL___ 144 P' 9 Va ~ RT RT Equation 3-3 J 0 - *544 _ 144 P' M PT Equation 3-32 Equation 3-33 P'Vtt = naMRT = na 1544T = 1544T Equation 3-34 . wa p'M P'M 2.70 P'S, 9 ~ V,, " 1544 T ~ 10.72 T~ T where: fi0 = wa/M -- number of mols of a gas Hydraulic radius* Equation 3-35 cross sectional area of flowing fluid Hydraulic radius = wetted perimeter Equivalent diameter: D = 4 times hydraulic radius (feet) d = 4 times hydraulic radius (inches) See page 1-4 for limitations. h H fm in SWMHiiiiMiiiiiiiT'i'ni i... i" nniTi i-fTinnwanwTWiimT^-- uM n iilt 3-6 CHARTER 3-fQRMUlAS AND NOMOGRAPHS FOR HOW THROUGH VAIVES, fITTINGS, AND PIPE Velocity of Liquids in Pipe The mean velocity of any flowing liquid can be calculated from the following formula, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. v = 0 83-3 -jqp * o-4o8 Q W = 0.0509 (For values of d1, see pages B-I6 to B-18) The pressure drop per 100 feet and the velocity in Sched ule 40 pipe, for water at 60 F, have been calculated for commonly used flow rates for pipe sizes of to 24-inch; these values are tabulated on page B-14. CRANE Exam pi* 1 Given: No. 3 Fuel Oil at 60 F flows through a 2inch Schedule 40 pipe at the rate of 45,000 pounds per hour. Find: The rate of flow in gallons per minute and the mean velocity in the pipe. Solution: /. p = 56.02 Connect ' Read 2. W = 45 000 p = 56.02 Q = 100 j- Q = 100 2' Sched 40 HO 11 OH II * Given: Maximum flow rate of a liquid will be 300 gallons per minute with maximum velocity limited to 12 feet per second through Schedule 40 pipe. Find: The smallest suitable pipe size and the velocity through the pipe. Solution: Connect Read /. Q = 300 V = 11 d = 3.2 2. 3y2' Schedule 40 pipe suitable 3- Q = 300 3 Y* Sched 40 Ik, Reasonable Velocities For the Flow of Water through Pipe Service Condition Reasonable Velocity Boiler Feed....................................... 15 feet per second Pump Suction and Drain Lines. . . .4 to 7 feet per second General Service............................... 10 feet per second City................................................. 7 feet per second Weight Density, in Pounds per Cubic Foot 3.8 __ ----------vntf CHAPTER 3-FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE Reynolds Number for Liquid Flow Friction Factor for Clean Steel and Wrought Iron Pipe CRANE Reynolds number may be calculated from the formula below, or, from the nomograph on the opposite page. The nomograph is a graphical solution o f the formula. 1 x> ab II 2 Xi o V 8 car.hsa o 8 u a 8 ji oc * s 5* js r bo u C aw a: Eu co >o 1&3C X3O S 8 al&) 3 s 1$ CO u u ,*8 CO CO (*\ CO c oc o. aa> <u o 2 a co vt; T3 U 4> > x: n ^O 3^ con -wo 4> 0 U, H 4*->? - X> C .2 1 i J= II J ^ ,2 (3(8 to, c co 3 Tu3 JZ <8 4> o S CoO 8 ">4T* O'! X0) .=BcOr &a>. 2 8J 5 a BO %r =8 3 -S t* 4) a TC3O 3C .coo < 4b)fi aCO U. c 4) -oCui co 4) 3 v u CoC T*">* ts.& i: c ll.p<i u w41 {-* *4-) A O 1o^0 LU C c 2 J o - > Reynold* Numberfoc LiquidFf&w*,- . ; Friction Factor for Clean Steel and Wrought Iron Pipe (continued) . looj 3iqno J3d spunoj ui 'XjlsuaQ it|8iaM - d eS S 8 a 1iiiiI ' ' ' i I ' ' ' ' I S3 S 1 1 1 1 1--II1i i i saqoui ui `adjd jo jajaiueja |BUiaju| - p n olm vi mi ui> i oio oi) Si iJ 2 S3 ~ =g -r satput u; `sdid ot ainpaqas jo az|$ laujuioj) S 23 2 SR 3 asiodjjuao ui `XjisoasiA ajniosqv - d p-mr1 |-Tm II I I I 1..I'I I ITI| 'I'll I'TTT 1 rMTITTT| I | I |l|l|l|ll`[ 1 1 II I Mll| I | I |l - -- --------------- - c-o c-r---i-n---<-a--r-*--f-lo----o-- a 8 9 S8I5S' 'i iA-,. m , inoji iad spunoj jo spuesitoqi ui *mo|J jo a*ea - M fe sS ffi? S .5 , Ss s s kst, si? s r . -? e -n o ^ 11I ftYirh HI lllft I I j linil 11 i i 11 I I I I I i ll^l KV'ii-h HI lllft I I I Innili I I II I I I ! I illrtll I I l.l.l.l LJ_ 1 L bltliLl.LJ_l.LLL 1 L_l t-llllll ip hi ?S 8 . SS S s ajnumuadsuo||E3 ui`mold joajau - $ III., f 1 S8.ss a a; f wv hf11 '11 itffr (11 * -ni mv\ * s > to ~ "3 ^ ^ - puooas Jad jaaj ojqno!'M0|d jo awt - & r* "! I' 8. i I * .* * Pressure Drop in Liquid Lines lor .Turbulent Plow CRANE CHAWBM- FOtMUlAS AND NOMOCOJHS FOE now THHOUGH VALVES; HTTINGS, AND PIPE Pressure Drop in Liquid Lines for Turbulent Flow (continued) "13-n s i--r i 11 | ii 111 i ) i i n~T 1 111 ' 1 111 ' l 1 I'11 I 1 111 r 1 111 1 i 1111 ' i n | <J . . . - ijoui ajenbs isd spunod u| j QOt Jad dojQ amsssJd -"W s L_l__ I--- 1--- L. lood ajqnO J3d spunod uj `Xjjsusa tqSiaM - d j__ i__ i__ l__ i___i__ i___L- _i___i___ i- i _i_____ i______ i______ L. _i----- 1----- 1 sapsui ui 'sdid )o jajauieia |euiaju| - p ` * ' r,i i_ s? s; rasas a s= n u in v cn ^ I__I__ I i i iI`i \ 1111 i1 1411 'i V \ t 'i *" |`"l[1.-lt| to u, ~ ~ CO l Jo 9d!d 0* 3InP3l|3S ass as ~ si: jo 3Z|S leujuioN o> a sO sO sO sO <o w pg s = <==><=,=, S3 g 8 S <= SSS sjnujw j0d suo||e3 u; `mou jo ajey 8S Scouo co cm Ja1 ** 8 g i 8 S11i ,r ,r .i `-SrrhnCO*-.*1to,1ri' ,Ii1`-i1ici-.*ci'oIi i`.1 hC1Mi1..1.i..1..1...--.|i..l1.C.ff.O..i..C.rO.....i. 1-C11',1CO11 CIM.....' .Ii--ng1,11 ,1>i1 ,, 1l1Mu-,'i i, S CO 1l1l|f ..Ai <,1,,1l|, JJ |j '<11', CM s s t| puooas J3d }33d oiQno ui `Mojd jo 3jey - j ^ _____________________________________________________ ___ J: I JOlOBd UOJJOJJd - / cira> McJj- C=O> CcMo So I ' ' ' ' I i i i ' I iIIII '' | 1 1 1II___ L- .... ..... 3-12CHAFTCK 3 -- FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPECRANE Pressure Drop in Liquid Lines for Laminar Flow Pressure drop can be calculated from the formula below, or, from the nomograph on the opposite page, only when the flow is laminar. The nomograph is a graphical solution of the formula. Flow is considered to be laminar at Reynolds number of 2000 or less; therefore, before using the formula or nomo graph, determine the Reynolds number from the for mula on page 3-2 or the nomograph on page 3-9. ._ ut; ufl uQ AP100 = 0.0668 -5- = 12.25 -37- = 0.0273 -~r dj d4 d4 (For values of ds and d\ see pages B-16 to B-18) Example 1 Given: SAE 30 Lube Oil at 60 F flows through a 6-inch Schedule 40 steel pipe at a rate of 500 gal lons per minute. Find: The pressure drop per 100 feet of pipe. Solution: 1. p = 56.02 page A-7 2. p -- 450 page A-3 3- R-c = 55 page 3-9 4. Since Re< 2000, the flow is laminar and the nomograph on the opposite page may be used. . Connect | Read P = 45 Index Q = 500 6' Sched 40 Index &Pioa = 4.5 Example 2 Given: SAE 10 Lube Oil at 60 F flows in a 3-inch Schedule 40 pipe at a velocity of 5 feet per second. Find: The flow rate in gallons per minute and the pressure drop per 100 feet of pipe. Solution: 1. p = 54*64 ........................... page A-7 2. Q = 115 page 3-7 3 P - 95 page A-3 4. Re = 1100 page 3-9 5. Since Rt < 2000, the flow is laminar and the nomograph on the opposite page may be used. Connect | Read P = 95 Index Q = 115 3 ' Sched 40 Index AjPioo -- 3*4 CRANE CHAFTEC3 --FORMULAS AND HOMOQRAFHS TOR FLOW THROUGH VALVES, FITTINGS, AND FIFE Pressure Drop in Liquid Lines for Laminar Flow (continued) Index 3-13 APioo 0.1 .2 .3-- .4 ,5 .6- *-.2 30-- 40 50 60 70 80 90 100-3 l- 3-14 CHAPTER 3 -- FORMULAS AND NOMOGRAPHS FOR PLOW THROUGH VALVES, FITTINGS, AND PIPE Flow of Liquids Through Nozzles and Orifices CRANE The flow of liquids through nozzles and orifices can be determined from the fol lowing formula, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. q -- 0.0438 d20 C'fhl = 0.525 cPo C A P p Q = 19.65 d20 CV/u = 236 d20 C Head loss or pressure drop is measured across the flange taps. Example 2 Given: The flow of water, at 60 F through a 6-inch Schedule 40 pipe, is to be restricted to 225 gpm by means of a square edged orifice, across which there will be a differential head of 4 feet of water. Find: The size of the orifice opening. Solution: 1. p = 62.34 ........................................... .. page A-6 2. p = 1.1 ............................................... .. page A-3 3. Re = 105 000 = (1.05 X lO5) .. page 3-9 4. Assume a ratio of do/dj, say 0.50 5. di = 6.065 ......................................... . .page B-16 6. d0 = 0.50 d\ = (0.50 x 6.065) = 7. C = 0.624 ........................................... .page A-19 Connect Read 8. q II C = 0.624 Index Si- Index Q = 225 do = 3" jo. An orifice diameter of 3 inches will be satisfactory, since this is reasonably close to the assumed value used in Step 6. 11. If the value of do determined from the nom ograph is smaller than the assumed value used in Step 6, repeat Steps 6 to to inclusive, using reduced assumed values for d0 until it is in reason able agreement with the value determined in Step 9. Su- I 1 | m a+ 1 IT. 1 71, | .Example 1 Given: A differential pressure of 2.5 psi is meas ured across the flange taps of a 2.000-inch I.D. nozzle assembled in a 3-inch Schedule 80 steel pipe carrying water at 60 F. Example 3 Given: A differential pressure of 0.5 psi is meas ured across flange taps of a 1.000-inch I.D. square edged orifice, assembled in i}4-inch Schedule 80 steel pipe carrying SAE 30 lubricating oil at 60 F. Find: The flow rate in gallons per minute. Find: The flow rate in cubic feet per second. l Solution: 1. di = 2.900 ........ 3" Sched 80 pipe; page B-17 Solution: I. P = 56.02 . 2. do/di = (2.000 -r- 2.900) = 0.69 2. di = 1.278 . .. 1H" Sched 80 pipe; page B-16 VJ 00 p II 00 1* 3. C = 1.07 . .turbulent flow assumed; page A-19 3- do/di = (1.000 4. p = 62.34..............................................page A-6 4 p = 450 .. .... suspect flow is laminar since viscosity is high; page A-3 Connect Read 5 C = 1.0 .. s- II bo t** : II ^ : 0 AP = 2.5 p = 62.34 Connect | Read v*> Index C = 1.07 do = 2.000 Index Q = 200 8. Calculate Re based on I.D. of pipe (2.900"). II t* 6. A P = 0.5 p -- 56.02 7 hL = 1.3 C.-- 1.0 Index 8. Index d0 = 1.0 q - 0.05 9. p = 1.1 ...................................... page A-3 to. Re = 200 000 . ................................... page 3-9 9- Calculate Re based on I.D. of pipe (1.278"). to. Re = lio ..........................................page 3-9 11. C = 1.07 . .correct for Re = 200 000; page A-19 it. C = 1.0 . .correct for Re = HO; page A-19 12. When the C factor assumed in Step 3 is not in agreement with page A-19, for the Reyn olds number based on the calculated flow, the factor must be adjusted until reasonable agreement is reached by repeating Steps 3 to it inclusive. When the C factor assumed in Step 5 is not in agreement with page A-19, for the Reyn olds number based on the calculated flow, it must be adjusted until reasonable agreement is reached by repeating Steps 5 to it inclusive. gjtei&WSw.*-- ?- CRANE CHAPTjr3 - FOtMULAS AND NOMOWtfWyOg HOW JHtOUQHVALViJsHTTINGS, AMX PIPt Flow of Liquids Through Nozzles and Orifices (continued) ,< 'l d0 3-TS* 3*16 ... CHARTER 3 --FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND FIFE Velocity of Compressible Fluids in Pipe CRANE a.'B g $ .2 al ^ g 1f ! 1 \ T3 S 0:1 02w0 x TJ Coo 60 w gS'S j? a-o > 0) xu CO > 8 5 0o p a u 1 ~ &| c oS'T. k<i J2 k> 33 " X u a c g"S 3 *tD/i 1 <5 X ^8 ua> a aC3 c 6C0 '35 3 3 'T vO IZ**.a -o 2 +-> 3 *G O 0 0 nO 1"H twiM3-Q*3 SCO .is p u <C 6 4) X fc s"5. ^-s a E S 3 0 *> ac 4-> J .2>> ui 0<g C\ tV.S 3 II II CL The mean velocity o f compressible fluids in pipe can be computed by means o f the following formula, or, by using J3 a CkO. i 'B S3 aE v i? 22 u l> -kCu> ozc. co 22. x8 'g % > Uo o *5 oC &260 V CO S eo 00 ci 4o-1 c6 8 v--O W) *vo 3 C0O0 ^ cE fai waM) 0Q0 O= 8 ^> 3 .5 a> S'!-* a 85 3 42 X c i a.3 o ^ as 8 _<Qc 4-> ^ -- c-- S 2 a <n ^ a "5. UExoI So, cn o 5H O u C. 0*T0`ok. 0O 5-o \J CO *U 4oJ c8 fT' "I Own a c S *0 0 e4ff)l S* 3OW <0 CO CRANE CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR HOW THROUGH VAIVES. FITTINGS, AND PIPE Velocity of Compressible Fluids in Pipe (continued) 3-1F Index jnoH Jad spunod jo spuesnoqi u; `o|d jo a}ey - ^ . i i g J 8 S S S? 852 2 CO <o u, ,r co cm3 ill I I I I I I I I ' 1 ' I I IIII I Ill'll I 11 I I I 1 I I I 1 I I I Ini i IiiiiIii II 1 1 I I I-L-Li I l 1111 1 Lllu 11 i i i I ^ 8n8r8r8i1 aimWCi'OFCMr --nmO* i CrM n-J ajnOjH'jad }aaj jo spuesnom ui `Xiiao|3A - Ji }ooj oiqnO jad spunoj in `Xijsuaa li|3i0M. * d </> 0033 OO a09 03 to e 09 J-- I 3-18 CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE_____________ CRANE Reynolds Number for Compressible Flow Friction Factor for Clean Steel and Wrought Iron Pipe 1 i -i*. CHAPTB 3 -- FORMULAS ANP NOMOGOPHS FO flOW THHOUGH VALVES. FITTINGS, ANDPIPE Reynolds Number for Compressible Flow Friction Factor for Clean Steel and Wrought Iron Pipe (continued) 3-1* S3i|3U| ut `adid ov a|npat|3S jo azis leutuioN fO S IS a J___ L| | | | |'| | | |'l | I |"I'TI T|'l I I I | ^1 J I I |^| 1^1I IM I I f "I I T't I "j 11` I 1 I I | lU m q r~ CO en < U) tO h CO A 11 i1 i m | n"TT| as sj s saqaui ui `adid jo lajauietQ |euraju| - p TT so>. 3I 1 *I^j1csI ic'"oi ^' toP<'lor1 ^'I''"cI oHo11c'T 1 ` I I u|j I I M g>I I I 3 o o 3 S 5 5 3 3 o . oS i 7"Hi r| i i i"r|-rrrT| 35s =*. =. <=. asjodjjuso uj M)jS03SjA ajn|osqv - ft Index Friction Factor for Clean Steel and Wrought Iron Pipe TTTTm rpTT I ii 11 [ 11 ii 1 8 s inoH iad spunoj jo spuesnoqi u| `moij jo ajBjj - ^ - I |i|iji|T|'i|H"i |IIII|I n e'|i|i|.i|n>|r| 1 |TITTTF-I 1-mnrp-iiiTf I | SSSS5SS a = <D <o w ** -- "J "> r m. I 3-20 CHAPTER 3-FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, fITTINGS, AND PIPE Pressure Drop in Compressible Flovy Lines CRANE X -O 030 CO X0c "Occq 4-> 4-> CO is8 1C S' Um 8 v8 -- >> <*- *-> 2 S wg& >SP o a 4_) --i a CO u 4a<>> r* w a" aw CO o sib* 603 5 --. X hx S lt & co 2 xv *w_> ^ O ,4> a C *7 o o 2 C.X8 "C xJ3 W CO c u a 4> X *o c CO u D X u 4) a *D a a c 2A5 > <n 4> -u a H TauJ c 23CO fVct f'l W"\ all -- abcoO a o A s >. --O --O cO<\ *o II H ii II a. *- O. N4 Read Index 2 Index i [ 00 \D o II o e cC < 4) a a ooo TJ o 4> X II ii y <8 *x Q. f! 00 <s M X4> X 4) o -n ii c c NO JSi .. co fix a (0 ,C 91 u tC3 u- SOf> e 43 3 * 8 M- *'iHX a.2 So f3i co 3 - cw><:>2 *A.a} E U O 9 o is <n,2 - O o 0`S Q,X 43 Z u g "S O TJCru 43 S = 3 <|2 *T*") XD2 ,_.Sov> & jg J e h 2c M Q. I* CO C VoN S o\ o * o, a. << u CO a. uc 2-8 f && CO u MO all R'S Si c CO bfi 2 as 5Or S' 8 CO _ S o 43 o X b > b a all X3 p io 43 1b3C S-S sCO a a> cC 5"5 r 43 U >> "3 <0 5P o w S,vco 4*-> 8 c "a > Ji CuO .9 o Xa <0 S-s 4. NOtx, O a*2. ._ 4a3 . o' _-a oc o- o ,, S3 2 f Sc6 2<=: o 43 6O0 x--.s 5 "2 lg C "2SCOc-O xu^ ?gu <0 4-> X 43 o 60 <0 u, b a * &8" < 2u, _L o s > a .. i8 ai <: wo m ^ N*_ a a bO a gaa SP o a n. <8 43 U. IS ou o 4-> 4) 4> < w -o c CO 43 a ,6TM0 ;a C/3 CLiTT o a 00 |3 wy W a o u4> 3 8 4) O. 4> O ci Oc*`n -- CO o o o' o' J= u a CO O E0 X Q.sX 4> ui a H o c s; C TS Jto = ^1^. s N f-1 "R- 5 6. / CRANE CHAPTER 3 - FOMfflbkS- AWO NOftOOKAMS fOt FtOVf THHOUGH YAltg, HTTINCS, ANO PlfE Pressure Drop in Compressible Flow Lines (continued) 3-2f ^0 JnoH iad spumy 0001 u! `MU i i Si i S S 5 " S Soo 10B n CM . . oo. u)tA m <si . Ill II I lililil il . I . I | I,.., |l)r.ii I ilililil I I-lI ill I Ml I III I III n I lilil lI i I i 1 i I I In I I limit 11 I l.l .1 I ,| , | , | , I,III IJ jojoej uoipuj-/^ ss s ss ^ i''i'' iin'' ' i' i' ' i ' ii (Ofr 8|npaqo$ -adid pjepuejs) saqaiq u; ` jajaiuetQ jeututofg CM CM p-hS*4 OO tO W d1 COCO CM CM -h i T* *7 |^ 111 i 'i |/i )i ] i \ f * ||| i fi 11 \ i '| i *|'irrtj 11 r i 1111 i 111 i i'|i | ry r\ i'| i | i [i'ih [i'i i q OO 00>eON(0 LO CO CM * pHO)OON.tO to ^ CO "~ s3i)ou| uj `ady jo ja^aiueiQ |euj3ju| --/> ' qoiq sjenbs J3d spumy ui `jasj 00I J3d dojQ ajnssay--"VV ^ tC5 to N oo O* ^J CM OO *0* to AO I**- OO 0> 2 2 ^ m , S <3 .1 1 1 1 11I t l t I . / * I L I ill I lililil y I t I I I I I t I i I I t i I I [ v I i l_l I i I I I I i i I i t t_t I i i I i I.lliiI i I i t I li i I (S X 4 punod J3d )33-j aiqno u; 'piny Suimoij jo 3Uin|0A agiaads-4 9- n CM CM p-, 0)00 N to lA ^ CO , CM |'t'i1HfjJiniiiiiiJi i mi.i Ijl i.ii -IHil i.l.i ,1 ,i.l, ii1i'iI)4Ji hl'l'f1/ i !|' 1(l<LI|'li`nLI[I'Il W i'V|'i |'|J`|11-1v1V11i1ii'i^I |1i |l|i1ililifl1'.iH1-.|11LVli 11f1,lll| 3 3S rH CM CO IA (O r* OOCTJ J2 CM * CO M* tft }ooj aiqno jad spunod ui ` Ajisuag iq3|9M --d 1--awgajg;j <`JJ'on 'A** 3-22 CHAPTER 3 -- FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, T1TTINGS, AND PIPE Simplified Flow Formula for Compressible Fluids Pressure Drop, Rate of Flow, and Pipe Size CRANE The simplified flow formula for compressible fluids is accurate for fully turbulent flow; in addition, its use provides a good approximation in calculations involving compressible fluid flow through wrought iron or com mercial steel pipe for most normal flow conditions. If velocities are low, friction factors assumed in the simplified formula may be too low; in such cases, the l) formula and nomograph shown on pages 3-20 and 3-21 may be used to provide greater accuracy. The Darcy formula can be written in the following form: APioo = W<0>-.000^3636//)) v = (^o-^Hbooo/^ Values of Ci W Ci Ci = Vi^io-8 n 336000/ Cs = ----- ^------ The simplified flow formula can then be written: APioo = C,C*V = ClCi P Ci = APlOO CjV APioo P Ci q _ APioo _ APioo P CiV Ci Ci = discharge factor from chart at right. t Ci -- size factor, from table on next page. The limitations of the Darcy formula for compre sible flow, as outlined on page 3-3, apply also to the simplified flow formula. Example 1 Given: Steam at 345 psig and 500 F flows through 8-inch Schedule 40 pipe at a rate of 240,000 pounds per hour. Find: The pressure drop per 100 feet of pipe. Solution: Ci = 57 C2 = 0.146 V = 1.45 .............. page 3-17 or A-15 APioo = 57 x 0.146 x 1.45 = 12 Example 2 Given: Pressure drop is 5 psi with 100 psig air at 90 F flowing through 100 feet of 4-inch Schedule 40 pipe. Find: The flow rate in standard cubic feet per minute. Solution: APioo = 5.0 Ci = 5-17 p = 0.564 .......................pageA-10 Ci = (5.0 x 0.564) -7- 5.17 = 0.545 W = 23 000 q'm = w -* (4-58 s,,) ........................... page B-2 q'm = 23000 -7- (4.58 x 1.0) = 5000 scfm For C2 values and an example on "determining pipe size", see the opposite page. 1 1 8 SS5 1 BI M"! fi 1A 1 1 1 1 1 1 1 1 Sfl \ CRANE CHAPTHt 3-- FOUMUtAS ANO NOMOGtAWS* fO* HOW THItOUQH VALVES, FITTINGS, AND FIFC 3-2? Simplified Flow Formula for Compressible Fluids Pressure Drop, Rate of Flow, and Pipe Size -- continued Nominal Pipe Size Inches Vs V* % Vt Vi 1 lVi VA 2 2% 3 3% 4 Schedule Number 40s 80 x 40s 80 x 40s 80 x 40 s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80 x 160 ... XX 40s 80s 160 ... XX 40 tc . 80 *- .. 40* 80* 120 160 ... XX ' Value of Cj 7 920 000. 26 200000. 1590 000. 4 290000. 319 000. 718 000. 93 500. 186 100. 4 300 000. 11180000. 21200. 36 900. 100 100. 627000. 5 950. 9640. 22 500. 114 100. 1408. 2110. 3 490. 13 640. 627. 904. 1656. 4630. 169. 236. 488. 899. 66.7 91.8 146.3 380.0 21.4 28.7 48.3 96.6 10.0 37.7 5.17 6.75 8.94 11.80 18.59 Nominal Pipe Size Inches Values of C2 Schedule Number Value of Ci 5 40s 1.59 80 x 2.04 120 2.69 160 3.59 ... XX 4.93 6 40 s 0.610 80 x 0.798 120 1.015 160 1.376 ... XX 1.861 8 20 0.133 30 0.135 40 s 0.146 60 0.163 80 x 0.185 100 120 140 ... XX 160 0.211 0.252 0.289 0.317 0.333 10 20 0.039 7 30 0.0421 40s 0.044 7 60 x 0.051 4 80 0.056 9 100 0.0661 120 0.075 3 140 0.090 5 160 0.105 2 12 20 0.015 7 30 0.016 8 ... s 0.017 5 40 0.018 0 ... X 0.019 5 60 0.020 6 80 0.023 1 100 0.026 7 120 0.031 0 140 0.035 0 - 160 0.042 3 14 10 0.009 49 20 0.009 96 30 s 0.010 46 . 40 0.010 99 ... X 0.011 55 60 0.012 44 80 0.014 16 100 0.016 57 120 0.018 98 140 0.021 8 160 0.025 2 Nominal Pipe Size Inches 16 Schedule Number 10 20 30 s 40x 60 80 100 120 140 160 Value of Ci 0.00463 0.004 21 0.005 04 0.005 49 0.00612 0.00700 0.008 04 0.00926 0.01099 0.01244 18 10 20 .. 8 30 .. X 40 60 80 100 120 140 160 0.00247 0.00256 0.00266 0.00276 0.002 87 0.00298 0.003 35 0.00376 0.00435 0.00504 0.0057% 0.00664 20 10 0.00141 20 s 0.00150 30 x 0.001 61 40 0.001 69 60 0.001 91 80 0.00217 100 0.00251 120 0.00287 140 0.00335 160 0.00385 24 10 0.000534 20 s 0.000565 . . X 0.000597 30 0.000614 40 0.000651 60 0.000741 80 0.000835 100 0.000972 120 0.001119 140 0.001274 160 0.001478 Note The letters s, x, and xx in the columns of Schedule Numbers indicate Standard, Extra Strong, and Double Extra Strong pipe respectively. Example 3 Given: An 85 psig saturated steam line with 20,000 pounds per hour^flow is permitted a maximum pressure drop of 10 psi per 100 feet of pipe. Find: The smallest size of Schedule 40 pipe suitable. Solution: AP100 = 10 Ci = 0.4 V = 4.5 ...........page 3-17 or A-13 C2 = 10 -s- (0.4 x 4.5) = 5.56 Reference to the table of C2 values above shows that the 4-inch size is the smallest Schedule 40 pipe having a C2 value less than 5.56! The actual pressure drop per 100 feet of 4-inch Schedule 40 pipe is: AP100 = 0.4 x 5.17 x 4-5 = 9.3 _____* 3-24 CHAPTER 3 -- FORMULAS AND NOMOGRAPHS FOR FlOW THROUGH VALVES, FITTINGS, AND PIPE Flow of Compressible Fluids Through Nozzles and Orifices CRANE The flow of compressible fluids through nozzles and orifices can be determined from the following for mula, or, by using the nomograph on the next page. The nomograph is a graphical solution of the formula. w = 0.52.? YcPoC VAPpi = 0.525 Y<P0C^j^ wagauk..', 1891 YcP0C^~APj1 = 1891 YcPCyj^r (Pressure drop is measured across the flange taps) Example 1 Given: A differential pressure of 11.5 psi is meas ured across the flange taps of a i.ooo-inch I.D. nozzle assembled in a 2-inch Schedule 40 steel pipe, in which, dry carbon dioxide (C02) gas is flowing at 100 psig pressure and 200 F. Find: The flow rate in cubic feet per hour at stand ard conditions (scfh). Solution: i- R = 35-1 ) 2. S,, = 1.516?...................... for COj gas; page A-8 3. k = 1.28 / Steps 3 through 7 are used to determine the Y factor. 4. P\ = P + 14-7 = 100 + 14.7 = 114.7 y. AP/P'i = 11.5 4- 114.7 = 0.1003 6. di = 2.067 .............. 2' Sched 40 pipe; page B-16 7. do/di = 1.00 4- 2.067 = 0.484 3. Y = 0.93 ....... ................................. page A-20 g. C = 1.003 . .turbulent flow assumed; page A-19 10. T -- 460 + / = 460 + 200 = 660 11. Pj = 0.71 ..............................................pageA-10 Connect Read 72. > II Pi = 0.71 Index 1 n- Index 1 C = 1.003 Index 2 14. Index 2 do = 1.000 Index 3 IS- Index 3 y = 0.93 W = 5000 16. q\ = 44 000 scfh ............................. pageB-2 77. ft ~ 0.018 ............................. page A-5 18. Re = 860000 or 8.6 x 106 ..............page 3-21 79. C = 1.003 is correct for Re = 8.6 X lO6 ...page A-19 20. When the C factor assumed in Step 9 is not in agreement with page A-19, fr the Reyn olds number based on the calculated flow, it must be adjusted until reasonable agreement is reached by repeating Steps 9 through 79. Example 2 Given: A differential pressure of 3 psi is measured across the flange taps of a 0.750-inch I.D. square edged orifice assembled in l-inch Schedule 40 wrought iron pipe, in which, dry ammonia (NH) gas is flowing at 40 psig pressure and 50 F. Find: The flow rate in pounds per second and in cubic feet per minute at standard conditions (scfm). Solution: R = 90.8 1 Se - o. 587 >......................for NH Sas* pas A'7 k = 1.29 ' Step.-' 3 through 7 are used to determine the Y factor. P'1 = P + 14-7 = 40 + 14-7 = 54-7 AP/P\ - 3.0 * 54.7 = 0.0549 di = 1.049 .............. 1'Sched 40 pipe; page B-16 do/di = 0.750 4- 1.049 = 0.716 y = -0.98 ........................ ..................... page A-20 C = 0.702 . .turbulent flow assumed; page A-19 70. T = 460 + t = 460 + 50 = 510 7 7. Pi = 0.17 ..............................................pageA-10 Connect Read 72 AP = 3.0 Pi = 0.17 Index 1 13 Index 1 C = 0.702 Index 2 14 Index- 2 do = 0.75 Index 3 15 Index 3 y = 0.98 w = 0.145 II 1 %A O 16 Index 3 y = 0.98 17 , qm = W 5*2'0-' --fTP- = - -6-7- f o" = ,1n95r. _ .page B-2 18. ft = 0.010 ............................................page A-S 79. R* = 310000 Or 3.10 x lO* .......... page 3-21 20. C = 0.702 is correct for Re = 3.10 X lO6 ..page A-19 27 When the C factor assumed in Steb 9 is not in agreement with page A-19, for the Reyn olds number based on the calculated flow, it must be adjusted until reasonable agreement is reached by repeating Steps 9 through 20. CRANE CHAFTETy-> FORMULAS AND HOMOQftAPHS FO FLOW THROUGH VALVES, FITTINGS, AND PIPE Flow of Compressible Fluids Through Nozzles and Orifices (continued) 3-2S S3 AP -600 --500 --400 -300 fc-200 F--150 do 6--1 5--1 H WfS ma C V t> 124U- .75- 13 1.2 .9 U 10- 10 .9 .Jh <5~H t Weight Density, in Pounds per Cubic Foot ta Of* ha da .55- .5 .45 .4 o a. .35 o aj uo * i O 7 8 9 10- .1 .09 .08 H'07 16--1--.0625 3-26 CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITTINGS, AND PIPE CRANE * to* _l_ a a _l_ _l_ Examples of Flow Problems Theory and answers to questions regarding proper application of formulas to flow problems can be presented to good advan tage by the solution of practical problems. A few simple flow problems were presented in Chapter 3 to illustrate the use of the nomographs. Other problems, both simple and com plex, are presented in this chapter. Many of the examples given in this chapter employ the basic formulas of Chapters 1 and 2; these formulas were rewritten in more commonly used terms for Chapter 3. Use of nomographs, when applicable, are indicated in the solution of these problems. The controversial subject regarding the selection of a formula most applicable to the flow of gas through long pipe lines is analyzed in Chapter 1. It is shown that the three commonly used formulas are basically identical, the only difference being in fie selection of friction factors. A comparison of results obtained, using the three formulas, is presented in this chapter. An original method has been developed for the solution of prob lems Involving the discharge of compressible fluids from pipe systems. Illustrative examples applying this method demonstrate the simplicity of handling these, heretofore complex, problems. 4-1 Reynolds Number and Friction Factor For Pipe Other Than Steel or Wrought Iron . The example below shows the procedure in obtaining the Reynolds number and friction factor for smooth pipe (plastic). The: same procedure applies for any pipe other than steel or wrought iron, such as concrete, wood stave, riveted steel, etc. For relative roughness of these and other piping materials, see page A-23. ' Example 4-1 . . . Smooth Pipe (Plastic) Given: Water at 80 F is flowing through 70 feet of 2-inch standard wall plastic pipe, (smooth wall) at a rate of 50 gallons per minute. Find: The Reynolds number and friction factor. Solution: page 3-2 2. p = 62.19 ........................ 3 d = 2.067 ........................ .......page B-18 4 M = 0.85 ........................ 5 D\g * 50.6x, 50x62a-.-1--9-- 2.067 x 0.85 Re - 89 600 or 8.96 x 10* 6. / = 0.0182 for smooth pipe ... page A-24 4-2 CHAPTER 4-EXAMPLES OF FLOW PROBLEMS CRANE Determination of Valve Resistance In Lf L/D, K, and Flow Coefficient Cv Example 4-2 ... 1, L/D, and K from Cv for Conventional Type Valves Given: A 6-inch 125-pound Y-pattern globe valve has a flow coefficient, Cv, of 600. Find: The resistance coefficient K and equiva lent lengths L/D and L for fully turbulent flow. Solution: 1. K, L/D, and L should be given in terms of 6- inch Schedule 40 pipe; see page A-30. 2. K = 891 d4 . page 3-4 or A-32 3. d = 6.065 d4= 1352.8 D = 0.5054 d6 = 8206 *. K 891 x 13528 = 6002 g 35 LK 5` D~f ...........page B-16 fbased on 6' ' \Sched 40 pipe ......... page 3-4 f, f--nmc o. J ~ 0.015 _____ /for 6.065' I.D. pipe in fully \turbulent flow range; page A-25 li- 223 D / 0.015 8. L = = 223 x -554 = H3 Alternate solution: 9- j _ 74-3 d6 /CV ............ L- 74-3 x8206 113 0.015 x 6ooz .page 3-4 Example 4-3 . . . L, L/D, K, and Cv for Conventional Type Valves Given: A 4-inch 600-pound conventional angle valve with no obstruction in flat seat. Find: The .resistance coefficient K, flow coef ficient Cv, and equivalent lengths L/D and L for fully turbulent flow. Solution: 1. K, L/D, and L should be given in terms of 4-inch Schedule 80 pipe; see page A-30. ' D-145 3. d = 3.826 4 L = 46 3- K = 2.4 6. Cy = 280 ................................. . page A-30 ...................................................... page B-16 ............................................page A-31 . .based on 4' Sched 80 pipe; page A-3I ......................................................page A-32 Example 4-4 . . . Venturi Type Valves Given: A 6 x 4-inch 6oo-pound steel gate valve. Find: The valve resistance coefficient K, and the equivalent lengths L/D and L, for fully turbulent flow of Reynolds numbers indicated on the Moody Friction Factor diagram; see page A-25. Solution: 1. K, L/D, and L should be given in terms of 6- inch Schedule 80 pipe; see page A-30. 2. For venturi port gate valves: ().-(&4 (L\ _ (L\ (da)4 \Dj- \D/> (d)4 .page 3-5 3. For 6-inch Schedule 80 pipe d = 5-761 D = 0.4801 ...................... .page B-17 d4 = 1101.6 4. For 4-inch Schedule 80 pipe: d = 3.826 d4 = 214.33 .page B-17 L 5- D = 13 for 4' constant diameter port gate valve; page A-30 ft).- 66.8 7. K-/ .for 6' Sched 80 pipe ................... page 3-4 0t 8. / -- 0.0151 Ifor fully turbulent flow, ........... Sched 80 pipe; page A-25 9. K = 0.0151 x 66.8 K = l.Ol or say 1.0 . .based on 6' Sched 80 pipe -ft)10. L = () D = 66.8 x 0.4801 L = 32.1 ........................ for 6* Sched 80 pipe CRANE -.-raSKv CHAPTSt 4 - EXAMPLES OF HOW FHOHEMS Check Valves -- Determination of Size Exampl* 4-5... Lift Chocks Given: A globe type lift check valve with a wing- guided disc is required in a 3-inch Schedule 40 horizontal pipe carrying 70 F water at the rate of 100 gallons per minute. Find: The proper size check valve and the press ure drop. The valve should be sized so that the disc is fully lifted under normal flow conditions; see page 2-7 for discussion. Solution: 1. Solve Darcy Equation for d*: 0.000 017 99 f(L/D)pQ2 A P d4 0.000 017 99 f(L/D)pQ2 d4 AP . page 3-4 Calculate Reynolds number to determine the friction factor based on flow in 3-inch pipe. 50.6 Qp Re = dp. 3- AP = 2.0 4- L/D = 450 5- P = 62.27 6. d =* 3.068 ....... ....... ....... ....... 7- p = 0.95 ....... 50.6 x 100 x 62.27 8. Re = Re = 108 000 or 1.08 x 106 / = 0.021 .......... .page A-25 10. ^ _ ,00001799 x .021 x 450 x 62.27 x lOO8 d* = 52-9 11. Referring to page B-16, note d* is 37.161 for the 2j4-inch Size and 88.605 fr the 3-inch size. It is evident that for this flow condition, the pressure drop through a wide-open valve is more than 2.0 psi for the 2j^-inch size and less than 2.0 psi for the 3-inch size. Therefore, the 3-inch valve would not be fully lifted and a 214-inch size should be used.. " 12. page 3-5 *3- =45 page A-30 14- (dtt)* = 88.605 if- (db)* = 37.161 16. / L\ 450 x 88.605 VdA = -ITTibr = 1075 page B-16 page B-16 17- p _ .00001799X.Q21 x 1073 x62.27 x `Qi 88.605 AP m 2.85 Example 4-6.. .In-Line Ball Checks Given: A 600-pound steel in-line ball check valve (page A-29) is required in a 2-inch pipe line carry ing 48 degree API crude oil at 150 F at a rate of 37 gallons per minute. Find: Theproper size check valve and the press ure drop yith the valve installed in both vertical and horizontal positions. The valve should be sized so that the disc is fully lifted under normal flow conditions; see page 2-7 for discussion. Solution: Procedure is same as for Example 4-5. 1. AP = 2.5 AP = 0.25 ........ vertical position; page A-30 . .horizontal position; page A-30 2. L/D =150 ........................................page A-30 3. S values for 48 degree API crude oil: 5 = 0.788 at 60 F; 0.75 at 150 F...page A-7 4. p = 62.4 x O.75= 46.8 .......... page A-7 /. Sched 80 pipe used for calculations... page A-30 6. d = 1-939 ........................................pageB-I7 7. p= 1.1 at 150F ......................... page A-3 8. Re, = x ?7 x 1.939 x 1.1 = 41 looor4.11 x 104 9 /= 0.025 2'Schec 30 pipe; page A-25 10 For valve in vertical position: ^4 _ .ooo 017 99 x .025 x 150 x 46.8 x 372 ~ d4 = 1.73 i-5 11. For valve in horizontal position: ,4 _ .ooo 017 99 x .025 x 150 x 46.8 x 372 ~ 0.25 d* = 17-3 d* = 0.8387 ........ for 1' Sched 80 pipe;.page B-16 d* = 2.6667 .... for 1Sched 80 pipe; page B-16 d* -- 14.136 ........ for 2' Sched 80 pipe; page B-17 d* = 29.117 ___ for V/i Sched 80 pipe; page B-17 13 As explained in the solution to Example 4-5, it is obvious a 1-inch valve in a vertical position and a 2-inch valve in a horizontal position are the largest sizes that can be used to assure "full-open" valves at specified flow conditions. 14. Pressure drop through 2-inch valve in a 2- inch pipe line: = -000017 99 x -Q2-5 x 150 x 46.8 x 37* - 14-136 AP = 0.306, or say 0.31 if Pressure drop through l-inch valve in a 2inch pipe line: (L\ 150 x 14.136 _ 0 wA= 0.8387 = 2528 ., -page M Ap - -000017 99 x .025 x 2528 x 46.8 x 37* ~ 14.136 AP = 5.15, or say 5.2 4-4 CHAPTER * - EXAMPLES OF FtOW PROBLEMS Laminar Flow in Valves, Fittings, and Pipe CRANE In flow problems where viscosity is high, calculate the Reynolds Number to determine whether the flow is laminar or turbulent. I Example 4-7 Example 4-8 - Given: Bunker C fuel oil at 90 F is flowing through a wide open 5-inch, 150-pound steel gate valve at a rate of 400 gallons per minute; the face to face di mension of the valve is 1 o inches. Find: The pressure drop through the valve. Given: S.A.E. 70 Lube Oil at 100 F is flowing at the rate of 600 barrels per hour through 200 feet of 8-inch Schedule 40 pipe, in which an 8-inch conventional globe valve is installed. Find: The pressure loss through the pipe and valve. r Solution: Solution: 7. li - 3000 2. n R` 50.6 Qp dp ......... ......................page A-3 ....... 3 <S = 1.014 at 60 F S = 1.000 at 90 F .. estimated; page A-7 7. M = 470 .................................. .page A-3 2. 35-4 < ............................ . page 3-2 3- 5 = 0.916 at 60 F ................ . page A-7 JT 3r 11 4 p - 62.4 x 1.000 = 62.4 ' .........page A-7 5 = 0.90 at 100 F ................ . page A-7 1 5 Calculations should be based on 5-inch 4- p = 62.4 x 0.9 = 56.2 ............ .page A-7 Schedule 40 pipe; refer to page A-30. 5- d = 7.891 ............................... .page B-16 s 6. d = 5-047 ........... ......................page B-16 D = 0.4206 ........... D = 0.6651 ............................... .page B-16 w* S-M- ' d3 = 128.56 ............ d4 = 4057-7 ............................... .page B-16 I 7- p 50.6 x 400 x 62.4 83.4 e ~ 5.047 x 3000 ~ 6. H * 35-4x600x56-1 7.981 x 470 0 8. Rt < zooo indicates the flow is laminar; therefore, use the following formula: 7- Re < 2000 indicates the flow is laminar; therefore, use the following formula AP - 0.000 0228 (jj'j ........ :5'4 Aa Pn = 0.000 191 --pjLjB-- .page 3-2 9 (5).-(b), IO- ............ ................... page A-30 Determine L, the equivalent length of the valve in feet: 12. L = D = i-o8 x 0.4206 = 0.454 feet 13. The actual face to face of the valve (L = 10 -T- 12) equals 0.833 feet. When the actual length of the valve flow path is greater than the equivalent length, the actual length should be used; refer to page 3-4. 4, - A r> AP = o.ooo 022J8(o-^8333^^(30-0i02gx-546o')\ A P = 0.421 8. D = 340 . .for conventional globe; page A-30 (d), (d)., 1 RD< 1000 ............... page 2-11 or 3-4 340x3*8 =io8 \D/, 1000 Then, 108 diameters of 8-inch Schedule 40 pipe is the equivalent length of globe valve at this laminar flow. 10. L 108 x 0.6651 =71.8 11. The total equivalent length of the valve plus the pipe equals 71.8 + 200 = 271.8, or say 272 feet. 12. o.ooo 191 x 470 x 272 x 600 AP = 4057-7 AP = 3.6 t CRANE CHAPTEK 4- examples of flow problems Laminar Flow in Valves, Fittings, and Pipe continued In flow problem* where viscosity is high, calculate the Reynolds Number to determine whether the flow is laminar or turbulent. Example 4-9 Given: S.A.E. 70 Lube Oil at 100 F is flowing through 5-inch Schedule 40 pipe at a rate of 600 gallons per minute, as shown in the following sketch. 4-5 i I <* Plan view of a horizontal piping system Find: The velocity in feet per second and pressure drop between Bourdon pressure gauges Pi and P2. Solution: 1. v = 0.408 d? Q . page 3-2 2. d = 5.047 .page B-16 D = 0.4206 .page B-16 d2 = 25.47 .page B-16 d4 = 648.72 .page B-16 V = 0.408 x 600 = 9.6 25.47 4 fi - 480 ...................................... page A-3 5 Calculate Reynolds number to determine if flow is laminar since the viscosity is high. 6 R. = 50.6 Qp dn .................. .page 3-2 7 = 0.916 at 60 F .............. page A-7 S = 0.905 at IOO F ` page A-7 8 p = 62.4 X 0.905 = 56.5 page A-7 9 R _ 50-6x600x 56.5 = 8 . 5.047 x 480 10 Re < 2000 indicates the flow is laminar. it A n 0.000 273/* L Q .................. page ,,3-2,, L 12 D=l? _ ! valve with tur bulent flow; page A-30 n- d = 2 /for 90 long raaius elbow; /turbulent flow; page A-30 14. L D i45 _ /angle valve without disc guide, ' '/with turbulent flow; page A-30 15- Sum of L/D for gate valve, long radius elbow; and angle valve, based on turbulent flow: --L = 13 + 20 + 145 17a8 16. For laminar flow: /_L\ = /_L \ JL_ \D/, \D/t 1000 .page 3-4 Gsl)().-178 ,i6 /sum for elbow, /gate, and angle -()D =l17- 126 x 0.4206 L = 53-0 feet ...........of 5' Sched 40 pipe 18. Length of straight pipe: 175 + 75 + 5 = 3oo feet 19. Total equivalent length of pipe plus gate valve, long radius elbow, and angle valve: 300 + 53.0 = 353.0 Ap = o.ooo 273 x 480 x 353 x 600 = 42.g 648.72 " 4-6 CHAPTER 4 - EXAMPLES OF FLOW PROBLEMS Pressure Drop and Velocity in Piping Systems CRANE '........ ...-- ExampU 4-10. ..Valves, Fittings, and Pipe--Steam Given: Superheated steam, at boo psig and 850 F, is flowing through 400 feet of horizontal 6-inch Schedule 80 pipe at the rate of go,000 pounds per hour. The pipe contains three long radius 90 degree elbows, one 6 x 4-inch venturi type gate valve which is fully open, and one Y-pattern globe valve having its stem 45 degrees from the run and its disc fully lifted. Find: The pressure drop through the piping system. Solution: 1. AP = 0.000 003 fLW*V 36----- ..page 3-2 or 3-20 W Re = 6.31 -3-- dp *-()D ............................ page 3-2 or 3-18 2. d = 5.761 ___ :............................. page B-l7 D - 0.4801 . ..................................page B-17 d6 = 6346 . ......................................page B-17 3. p = 0.029 ...................................... page A-2 r, 6.31 X 90 OOO ji, /\< -- , ~ 5.761 x 0.029 Re = 3 400000 or 3.4 x io* 5. / = O.Ol 5 ......................................page A-25 . L ,,,, ,, ,, /for 3 long radius ) ~ 20 x 3 60 .......... (elbows; page A-30 ^ = 145 ... .for Y-pattern globe; page A-30 -- -- AA R ) DD' / for 6 x 4' venturi type ...........\gate; Example 4-4, page 4-2 7. Sum of L/D for the three elbows and two valves: = 60 + 145 + 66.8 = 271.8 ` 8. Sum of L for the three elbows and two valves; L - = 271.8 x 0.4801 = 130.5 9. Total equivalent length of pipe plus elbows and valves: L = 400 + 130.5 = 530.5, or say 531 jo. V = 1.215 at 614.7 psia and 850 F ` .................. page A-17 or 3-17 .ooooo336x.qi5x53i x9QOoo2xi.215 1' ~ 6346 AP = 41.5 Example 4-11.. .Flat Heating Coils--Water Given: Water at 180 F is flowing through a flat heating coil, shown in the sketch below, at a rate of 15 gallons per minute. Find: The pressure drop from Point A to B. Solution: 1. AP = 0.000 2i6;fLpQ* d page 3-2 Re = ^ dp ................... page 3-2 or 3-8 D 2. p = 60.57 page A-6 3 d= 1.049 d5 = 1.270 .. .page B-16 D = 0.0874 page B-16 4 p = 0.34 5- = 50-6 X 15 X 60.57 e 1.049x0.34 Re = 128 900 or 1.289 x io5 page A-3 6. / = 0.024 ................................. page A-25 7. Length,-straight pipe (see sketch) = 18 feet 8. r/d = 4 9. Total resistance for one 90 degree bend: L/D = 13.5 page A-27 10. The total resistance for one 180 degree bend is the resistance for the 90 degree bend (L/D = 13.5), plus the resistance due to length (L/D = 7.5), plus one-half the resistance due to bend (L/D = 6 -5- 2 = 3.0), or a total of 24.0. 11. The total bend loss, L/D, is: Two 90 degree bends. .. .2 x 13.5 = 27.0 Seven 180 degree bends.. 7 x 24.0 = 168.0 L/D for total bends = 195.0 12. Total bend equivalent length in straight pipe: L = D = 195 x 0.0874 = 17 04 ij. Total equivalent length of pipe is: L = 18 + 17.04 = 35-04, or say 35.0 .poo 216 x .024 x 35.0 x 60.57 x 15* 14. AP = 1.27 AP = 1.95 1f frfrm ,,-,, ....... - - jiMiij i rWifraiTTfi iaw :^s-, CRANE __________________________________CHATTSE 4- tXAMfttS Of ROW ftOHIMS '* ' Pressure Drop and Velocity in Piping Systems _______ 4-r continued Example 4-12.. .Cylindrical Pipe Coil--Steam Given: Saturated steam at 150 psig is flowing through a cylindrical pipe coil, as shown in the sketch at the. left, at a rate of 2000 pounds per hour. The coil is made of 2-inch Schedule 4 steel pipe. Find;'The pressure drop from Point A to B. Solution: fLW2V AP = 0.000 003 36' ^-- . .page 3-2 or 3-20 6,31 w dn L-@)D .. .page 3-2 or 3-18 2. d = 2:067 d5 = 37.72 ... .page B-16 D = o. 1722 . ... .page B-16 3 p = 0.018 . .... page A-2 4 n R, = 6.31 x 2000 --z-------------- S = 339 000 or 3-39 x i' ,.5 5 / = 0.020 ........................................page A-25 6. Length of inlet and outlet pipe with slight bend (see sketch) equals 6.0 feet. 7 r/d = 15 8. Equivalent length of coiled pipe (page 2-12): ~D~ 41 /for one 90 degree ............................ \bend; page A-27 D=2M /for resistance due to length of ' \one 90 degree bend; page A-27 L 17-5 D~ * o ,, /resistance due to bend of one '75 \90 degree bend; page A-27 There are 6; 5 coils or twenty-six 90 degree bends in the coil. Then, the equivalent length of the coil is: ^ - (26-1) (23.5 + 8.75) + 41 = 847 -GO'- 847 xo.1722 =146 9 The total equivalent length of the coil is; 6.0 + 146 = 152 feet 10. V =2.757 ............................ page A-14 or 3-17 = .OOP 003 36 X .020 X 1 52 X 2OOP2 x 2-757 it. = 37-72 AP = 3.0 Example 4-13.. .Flow Given in Metric Units--Oil Given: Fuel oil, with a specific gravity of 0.815 and a kinematic viscosity of 0.027 cmVsec, is flowing through a 50 millimeter I.D. steel pipe of 30 meters length at a rate of 7,0 liters per second. Find: The pressure drop in pounds per square inch and in kilograms per square centimeter. Solution: AP = 0.000 216 M2 d6 ----- page 3-2 or 3-10 Re = 3160 vd ................... page 3-2 Convert units given to those used in this paper; refer to page B-10. 1 mm = 0.003 28 ft 1 m = 3.28 ft 1 mm = 0.039 37 in. 3 L = 30.0 m = 30.0 x 3.28 = 98.4 ft 4 d = 50 x 0.039 37 = `-97 *n- 5- p = 62.4 .S = 62. x 0.815 ___ page A-7 p = 50.9 Ib/ft3 6. 7.0 liters = 7.0 x 0.2642 * 1.849 gal .page B-l 1 7 8. v = 0.027 x 100 = 2.7 centistokes. .pg.B-3 9 Rne - 13--1-6--0---x---1--1-0- .29 = 6, 5 8_ 00 or 6, .58' x 104. 2.7 x 1.97 10. / 0.0230 . . page A-25 11. d6 = 1.97s = 29.6 _ .000 216 x .0230 x 98.4 x 50.9 x 1 IQ-92 12. ~~ 29.6 AP = 10.32 13 Pressure drop = 10.32 x 0.0703 = 0.725 kg/cm* . tot.. 4.8 CHAPTER 4 -- EXAMPLES OF FLOW PROBLEMS CRANE Pressure Drop and Velocity in Piping Systems -- continued Example 4-14.. .Bernoulli's Theorem--Water Given: Water at 6o F is flowing through the piping system, shown in the sketch below, at a rate of 400 gallons per minute. 5" Standard 90 deg Elbow \ 4" Schedule 40 Pipe -d 5" Schedule 40 Pipe / -150`- orn,o*. N.r5,," Schedule 40 Pipe ,,P, lElevation 75* Elevation Z.0' -no1- 5" x 4" Reducing 90 deg Elbow \ Find: The velocity in both the 4 and 5-inch pipe sizes and the pressure differential between gauges Pi and P%. Solution: 1. Use Bernoulli's theorem (see page 3-z): 11. 30x0.3355 = 10.07 /equivalent length in feet of 4' v . 144Pi . *l rr . 144 Pi . .l (Schedule 40 pipe ... for 4' elbow Zi + --- p5-l----- + ~2g -- A.2 + Since, pi = pt oPt + ~2g + hi L = D = 30 x 0.4206 = 12.62 /equivalent length in feet of 5' (Schedule 40 pipe... for 5' elbow rh +hi)7 v Pi - Pj - ((Zs - Zl) + 44 \ H / 12. For a 4-inch standard 90 degree elbow, nL L = 144 AP ................. f ........................ page 3-5 AP = (10.07 + 100) 3.68 = 0.371 ..page B-14 P 13- For 100 feet of 5-inch Schedule 40 pipe, AP = pressure drop due to flow AP = 1.19 ..........................................page B-14 L-(b)D 14- For-a 5-inch standard 90 degree elbow, AP = (12.62 4- 100) 1.19 = 0.150 ..page B-14 2. p = 62.34 ................................page A-6 3. Zi - Zi= 75 - 0= 75 4. Vi = 10.08 ............ in 4" pipe; page B-14 /. Vt =6.42 ............ in 5' pipe; page B-14 g P2 -- Pj _ 6.42* -- io.o82 ` 2g ~ 2 X 32.2 - = --0.938 or say --0.9 feet 7. Pressure drop through 100 feet of 4-inch Schedule 40 pipe is; AP = 3.68 ........................................page B-14 8. Then the pressure drop through 110 feet of 4- inch Schedule 40 pipe is : AP= -^x 3.68 = 4.05 100 .............. page B-14 _U_ 9- ) = 3 ........................ tfor 90 degree stand........................ \ard elbow; page A-30 jo. D = 0.3355 . .for 4'Sched 40 pipe; page B-16 D = 0.4206 . .for 5* Sched 40 pipe; page B-16 15 For a 5 x 4-inch 90 degree reducing elbow, AP = 0-371 * - -- = 0.261, or say 0.26 16. For the 5-inch Schedule 40 pipe, AP = /il__71^ 1.19 = 2.68 ..pageB-14 17. The pressure drop in the pipe between the gauges, due to fluid flow, is: AP = 4.05 .............. 110 feet 4'Sched 40 pipe A P = 0.26 .............. 5 x 4' 90 reducing elbow AP = 0.1 5 .................... 5" standard 90 elbow AP = 2.68 .............. 225 feet 5' Sched 40 pipe AP =7.14 (total) 18. /lt=144AP=i4iii7d4= ,6 - P 62.34 Pi - Pt - (~~~) (75-o " -9 + &-5) *9- Pi - P, = 39.2 .. . n it tTB Inr b 9 n 9 r r *3 N -*| i m* st CRANE CHAPTER 4 - EXAMINES OP FlOW PHOBIEMS 4-9 Pressure Drop and Velocity in Piping Systems -- continued Example 4-15... Power Required for Pumping Given: Water at 70 F is pumped through the piping system below at a rate of too ga1ll.ons per mi.nut,,e. 3" Schedule 40 Pipe . nElevation Z2=400 300' V _U 3" Standard Gate Valve 1! 1m nov Four 3" Standard 90 deg Elbows y J_____________ Elevation Z^O 1-7/30'- .-----------------70'----------------- - C K<" Globe Lift Check Valve with Wing Guided Disc Find: The total discharge head at flowing condi tions and the brake horsepower required for a pump having an efficiency of 70 per cent. Solution: 1. Use Bernoulli's theorem (see page 3-2): 144 Ft . v2i ^ , 144 Pi . vh , L Zi + -pr+rg-Zi+ P2-+Tg+hL 2. Since Pi = Pi and vx - v2, the equation can be rewritten to establish the pump head, H: -- (Pi - Pi) = (Zi - Zi) + hL p 3. hL= 0.1863 f Li? a ..........page 3-2 dv p R, = 123-9 P 0.408 Q v = --jr- page 3-2 or 3-8 page 3-2 or 3-6 K = /> then-^ = j .......... page 3-4 L - (L/D) D QHp brake horsepower = 247 000 ep .. page B-9 d = 3.068 D = 0.2557 ^=9.413 .. .page B-16 .......................... .. .page B-16 / v =0--.-4--0--8---x---1--0-0-= 4.33 9.413 6. p = 62.27 ............................ .page A-6 7 M = 0.95 ........................... 8. n 123.9X 3.068X4.33 X62.27 R`= 5^? .page A-3 Re = 107 900 or 1.079 x 105 9 /= 0.021 10. L D = 30 x 4 = 120 page A-25 or 3-8 for four std. 90 elbows; page A-30 11. D= 1073 . /for one V/2 globe lift check with '' \wing-guided disc; Prob. 4-5, Step 16 12. K = 1.0 .. .for exit loss; page A-26 n- L _ K _ t .000 D f 0.021 = 47-6 ................for exit loss 14. For elbows, valve, and exit loss, ^5 = 120+ 1073 + 47.6 = 1240.6 or say 1241 (jj)D= 124i x 0.2557 = 317 13. The total equivalent length of the pipe is: L = 30 + 100 + 70 + 300 + 317 = 817 16. The head loss due to the flow through elbows, valve, and pipe, and the exit loss is: , 0.1863 X O.021 x 817 x 4-332 h*--------------------3x568----------------= '9-53 17. The total pump head is: 400 - o + 19.53 = 419-53 or say 420 ft 18_. ,,, , 100x420x62.27 , Brake horsepower = 247 000 ^x 0.70 =15.1 Example 4-16.. .Air Lines Given: Air at 65 psig and 110 F is flowing through 75 feet of 1-inch Schedule 40 pipe at a rate of 100 standard cubic feet per minute (scfm). Find: The pressure drop in pounds per square inch and the velocity in feet per minute at both up stream and downstream gauges. ' Solution: /. Referring to the table on page B-15, read pressure drop of 2.21 psi for '.00 psi, 60 F air at a flow rate of 100 scfm through 00 feet of l-inch Schedule 40 pipe. 2. Correction for length, pressure, and temperature (page B-15): ap , (is.) ('?+ '*') (:&Ui) \ioo/ \ 65 + 14.7/ \ 520 / AP= 2.61 3. To find the velocity, the rate of flow in cubic feet per minute at flowing conditions must be determined from page B-i 5. ,, ( 14-7 \ (4^0+ t\ qm-qa\l4.7 + P)\ 520 ) At upstream gauge: 14.7 \/46o+no\ (----- -- Z~ ) l ---------------) " 20.2 14.7+65/V 520 ) At downstream gauge: r 14-7 1/460+no\ qm- 100[_14-7+(65-2.6i)J\ 520 / 2`9 4 V = ^ ......................................page 3-2 3. A -- 0.006 ......................................page B-16 6. V -- = 3367 ........ at upstream gauge \/ 10.0 'S AO'S V =-------r = 3483 0.006 .. .at downstream gauge Note: Example 4-16 may also be solved by use of the pressure drop formula and nomograph shown on pages 3-2 and 3-21 respectively or the velocity formula and nomograph shown on pages 3-2 and 3-17 respectively. CHAPTER 4 -- EXAMPLES OF FLOW PROBLEMS Pipe Line Flow Problems CRANE Example 4-17.. .Sizing of Pump for Oil Pipe Lines Given: Crude oil 30 degree API at 15.6 C with a viscosity of 75 Universal Saybolt seconds is flowing through a 12inch Schedule 30 steel pipe at a rate of 1900 barrels per 3 hour. The pipe line is 50 miles long with discharge at an elevation of 2000 feet above the pump inlet. Assume the pump has an efficiency of 67 per cent. Find: The brake horsepower of the pump. Solution: 1. fLpB A P = 0.000 1058 d5 ("Equation 3-5 on page 3-2 <or, after converting B to Q, (use nomograph on page 3-11 ! t = 1.8 tc + 32 ................................page B-10 KD = 35-4Bp^ ......................page 3-2 or 3-8 ' hL - ""*AP P ................... brake horsepower = --QUe-- r 247 000 ep 2. t = (1.8 x 15.6) + 32 = 60 F j- P = 54-64 S = 0.8762 .................................... ............................ ............... page B-7 4 d - 12.09 ............................ d6 = 258 304 ............................ 5- 75 USS -- 12.5 centipoise ....... 6. R 35-4 x 1900 x 54-64 24 300 e 12.09 x 12.5 7 / = 0.025 ....................................................page A-25 8. _ o.ooo 1058 x 0.025 x 50 x 5280 x 54.64 x igoo* 258 304 AP = 533 9 hL L = 1--4--4--X7--533 = .... *405 54.64 7 10. The total discharge head at the pump is: H 1405 + 2000 = 3405 11. 490^0 brfe)lN (v4^2bgsaryl\ (W~+nw< =1330 12. Then, the brake horsepower is 1330x3405x54.64 247 000 x 0.67 = 149b. or sav 1500 gin H U H ... inwissjMwsp w i i 'MI'lj'BliiW illW I CRAKE CHAfTM 4-EXAMHK OF HOW WOBtEMS Pipe Line Flow Problems -- continued 4-tr- - Exampl* 4-18.. .Gas Given: A natural gas pipe line, made of 14-inch Schedule 20 pipe, is too miles long. The inlet pressure is 1300 psia, the outlet pressure is 300 psia, and the average temperature is 40 F. The gas consists of 75% methane (CH), 21% ethane (CjH), and 4% propane (C3Hg). Find: The flow rate in millions of standard cubic feet per day (MMscfd). Solutions: Three solutions to this example are presented for the purpose of illustrating the varia tions in results obtained by use of the Simplified Compressible Flow formula, the Weymouth for mula, and the Panhandle formula. Simplified Compressible Flow Formula (seo pago 3-3) 7. 9 = 114-1 {P\Y - (P'2)2~| fLmTS, J d8 2. d = 13.376 .................................... page B-16 d6 = 428 185 ................ .................. page B-16 3- / = O.Oi 28. turbulent flow assumed; page A-25 4- T = 460 +1 = 460 + 40 = 500 5- Approximate atomic weights: Carbon........... C = 12.0 Hydrogen.... H = 1.0 6. Approximate molecular weights: Methane (CH) M = (1 x 12.0) + (4 x 1.0) = 16 Ethane (C2H) M = (2 x 12.0) + (6x1.0) = 30 Propane (CjH) M - (3 x 12.0) + (8 x 1.0) = 44 Natural Gas M = (16 x 0.75) + (30 x 0.21) + (44 x 0.04) M = 20.06, or say 20.1 o M (gas) 20.1 7- ... page 3-5 8. q'n = ,J- 3002 -- 3002) 428 185 114 \0.01 28 X 100 X 500 x 0.693 q h = 4 490 000 , = /4 490000 ft A /24 9- * \i 000 ooojpwy \ day / 107.8 to. = 0.482 q\S, ` dft ............. page 3-2 II. n = O.Ol 1 .......... estimated; page A-5 12* Ad j --. 0.....4. 82x4490, 000x0.601 13 376 X 0.01 l R, = 10 190 000 or 1.019 x 107 /= 0.0128 .................................. page A-25 14. Since the assumed friction factor (/ = 0.0128) is correct, the flow rate is 107.8 MMscfd. If the assumed friction factor were incorrect, it would have to be adjusted and Steps 8, 9, 12, and 13 repeated until the assumed friction factor was in reasonable agreement with that based upon the cal culated Reynolds number. Weymouth Formula (>0 page 3-3) 10. O. -1009 ............../use a slide rule or (logarithms, page B-12 \ 0.693 x 100 \5oo/ q'h = 4 380 000 18. q'd > r438aoooW\/^hr\ \i 000 000Jar/ \ day / Panhandle Formula (see page 3-3) MW ,5. 20. Assume average operation conditions; then efficiency is 92 per cent: E = 0.92 2/. d2-818* = 889 ............../use a slide rule or ..............(logarithms, page B-12 * - ,6.8xo** x885 (`^ -;<*) q'n = 5 570000 23. q't _ (5 570 000 ft,N\ (24 Jar\ _ ,, , \i 000 000Jar/ \ day / " (BP 4-12 rrifilifliai^f^if CHAPTER A-EXAMPLES OF FLOW PROBLEMS ^ Discharge of Fluids from -Piping Systems CRANE m Example 4-19. . Water Given: Water is flowing from a reservoir through the piping system sketched below. The reservoir has a constant head of 11.5 feet. Solution: Q = 19.65 cP^|'K K (day ............page 3-5 d2 = 9.413 d* - 88.605 y pipe; page B-16 .V pipe; page B-16 d4 = 18.25 .2' pipe; page B-16 4.' Tabulation of resistances, assuming fully tur- -ibulent flow, follows. Subscript "o'prefers to 3-inch size and subscript ">" refers to -the 2-inch size. (b). (blKa Reference Entrance loss Miter bend Gate valve 10 feet of 3-inch pipe Sudden contraction 0.5 1.0 0.23 0.7 58 13 39.1 0.23 page A-26 page A-27 page A-31 page A-30 page A-31 10 *7" 0.2557 page A-31 page A-26 Exit loss 20 feet of 2-inch pipe 1.0 page A-26 116.1 20 * 0.1722 2.2 page A-31 Totals 2.43 3.43 / Total Ka = 16.65 + 2.43 = 19.08 6. Q = 19.65 (9-413) j = >44 This solution assumes flow in the fully turbu lent zone per- page A-2 5, from which,/= 0.0175 for 3-inch pipe and 0.019 (r 2-inch pipe. 7. Check assumed friction factors used in de termining resistance of 2 and 3-inch pipe. 8. p -- bz.27 .......................................... page A-6 9. p = 0.95 .......................................... page A-3 10. Re = 150 OOO or 1.5 x 10s for V pipe; page 3-9 Re = 230 OOO or 2.3 x lO6 for 2' pipe; page 3-9 /= 0.020 ..................for y pipe; page A-25 / = 0.0206 ..................for 2* pipe; page A-25 11. Since assumed friction factors (Step 6) are not in agreement with those based on approxi mate flow (Step 10), total K values in Step 4 must be corrected by multiplying the values by the ratio of / based on approximate flow to / assumed. 12. Repeat Steps 5 and 6, using the corrected values of K. . Total K,, = 2.78 + 18.08 = 20.86 19.65 (9-413)137 13. Further determination of Reynolds number and friction factor based on the corrected flow rate obtained in Step 12 is not necessary, since the effect on friction factor would be negligible. Example 4-20.. .Steam at Sonic Velocity Given: A header with 170 psia saturated steam is feeding a pulp stock digester through 30 feet of 2-inch Schedule 40 pipe which includes one standard 90 degree elbow and a fully-open conventional plug type disc globe valve. The initial pressure in the digester is atmospheric. Find: The initial flow rate in pounds per hour, using both the modified Darcy formula and the sonic velocity and continuity equations. . ' Solutions--for theory, see page 1-9: Modified Darcy Formula /. W = 189! V................page 3-4 ................ ..page 3-4 2. k = 1.3 ..... ........... . page A-9 3- D = o.72i cP = 4.272 .page B-16 _L _ 30 D ~ 0.1722 174.2 .. .for pipe L D ^40r ` for V globe valve; page A-30 L D =3 ........ for V elbow; page A-30 5 /= 0.019 ----- ------ ffor fully turbulent \flow; page A-25 6. Sum of K for pipe, valve, and elbow: K = 0.019(174.2 + 340 + 30) = 10.34 7- K = 0.5 K = 1.0 ........ :... .for entrance; page A-26 ........ ..................for exit; page A-26 8. Then, for the total system* K = io.34+.o,f -+1.0-- n.84* g AP ^ 17b - 14-7 - 155-3 >0.914' Sonic Velocity and Continuity Equations 14- V, = V kg 144 P' V f `........................page 3-3 W = ---- V , 0.0509 V ........ Equation 3-2; page 3-2 if- P` = P\ - AP P' = 170 - 133-5 -- 3f>-5 , AP determined in Step 10. : , 16. h, = 1196 .. 170 psia saturated steam ;pafeA-I4 17 At 36.5 psia, the. temperature of steam with total- heat of 1196 Btu/lb equals1316 F, and V = 12.4 ...... v............... pages A-13 aqd A-I6 18. v, m V 1.3 X32.ZX 144 x 36.5 X 12.4. l65i 'f ' ,> 0.0509 X 12.4 ' \ t9" / \ jefr ' i it!1- & St, o 70. Using tl||||pi;onpageA-22 for k - 1.3, it is found- ir.78, the maximum AP/P'i is oi^^(mtrpofated from table on page A-22). Since hP/P\ is; fessthan indicated in Step 9, sonic velocity occurs attfte end-of the pipe, and AP ire the equation of Step`7 is: AP.= o.TSpx 170--1-33.5 77. Vi = 2.675 . - >_,.........- ......... page A-14 12. finterpolated from = 0-710 .............. " \table; page A-22 i8i xo.7t X4.272A/i---8-^;5675 W = 1178ft- . . - 4-14 CHAPTER 4 - EXAMPLES OF FLOW PROBLEMS Discharge of Fluids from Piping Systems -- continued CRANE Example 4-21.. .Gases at Sonic Velocity Example 4-22.. .Compressible Fluids at Subsonic Velocity Given: Coke oven gas having a specific gravity of Given: Air at a pressure of 19.3 psig and a tem 0.42, a header pressure of 125 psig, and a tem perature of 100 F is measured at a point 10 feet perature of 140 F is flowing through 20 feet of 3- from the outlet of a 3^-inch Schedule 80 pipe dis inch Schedule 40 pipe before discharging to atmos charging to atmosphere. phere. Assume ratio of specific heats, k = 1.4. .1 Find: The flow rate in standard cubic feet per 125 psig 2D' of 3" Schedule 40 Pipe .Z minute (scfm). Solution: 1. q'm = 678 YcP^^r^r ..........page 3-4 Find: The flow rate in standard cubic feet per hour (scfh). Solution--for theory, see page 1-9: , v ,, ZAP P\ /. q h = 40 700 ,, ....... page l-4 K = /-^ .......................................... page 3-4 2. P'i= 19.3 + 14.7 = 34.O 3. A P = 19.3 4. D= 0.0455cP = 0.2981 .............. page B-16 K-f D 2. P\ = 125 + 14-7 139-7 .page 3-4 $. f = O.0275 . .fullyturbulent flow; page A-25 , ,, , L 0.0275 X 10 , 6. K = f-p= 0.0475 =6'4 , forp,pe 3- /= 0.0175 . page A-25 K = 1.0 ........................ for exit; page A-26 m Note: The Reynolds number need not be cal K = 6.04 + I = 7.04 .......................... total culated since gas discharged to atmosphere through a short pipe will have a high Re, and AP 19.3 ,,, flow will always be in a fully turbulent range, 7 F5? - 34 568 in which the friction factor is constant. 4 D = 0.2557 cP = 9.413 .page B-16 ,,5- K= ,L JD = 0---.-0-1--7-5---X---2-0- 0.2557 = . 1.^369 . .for pipe 8. Y = 0.76 ........................... page A-22 9.. 7\ = 460 +h = 460 + IOO = 560 - ro. q'm = 678 x .076 x 0.2987 ^;3xx5' ;;0 K = 0.5 .................. for entrance; page A-26 K = 1.0 ..........................for exit; page A-26 q'm = 62.7 K= 1.369 + 0.5+1.0= 2.87 .......... total .6 AP _ 139.7 - 14.7 _ 125.0 0.895 P\ ~ 139.7 _ 139-7 7. Using the chart on page A-22 for k = 1.4, it is found that for K = 2.87, the .maximum AP/P'i is 0.657 (interpolated from table on page A-22). Since AP/P'i is less than indicated in Step 6, sonic velocity occurs at the end of the pipe and AP in Step j is; AP = 0.657 P'i = 0.657 x 139.7 = 918 .8 Ti = 140 + 460 = 600 9 Y = 0.637 . /interpolated from /table; page A-22 10. q\ is equal to: 40700x0.6, 37x9.413^/ ;9^1.8-X^601 039x-70.42 q\ = 1 028 000 k 1 1 A'- fc* 1 ft* I la CRANE nowchafte* * - examfies of MtostEMS Flow Through Orifice Meters 14-! Example 4-23.. .Liquid Service Given: A square edged orifice of 2.0-inch diameter is installed in a 4-inch Schedule 40 pipe having a mercury manometer connected between the flange taps. Find: (a) The theoretical calibration constant for the meter when used on 60 F water and for the flow range where the orifice flow coefficient C is constant . . . and (b), the flow rate of 60 F water when the mercury deflection is 4.4 inches. Solution - (a) 1. Q = zj6d?oCyj--~ .page 3-5 or 3-15 50-6 Qp R' = dp . page 3-2 or 3-8 2. To determine differential pressure across the flange taps, AP = ...A...l..i.n....p... . 12 X 144 .................................. page 3^-5, where: Ahm = differential head in inches of mercury The weight density of mercury under water equals pu(SBa - Sa), where (at 60 F): p,f = density of water = 62.34 .................... page A-6 SHa = specific gravity of mercury = 13.57 . .page A-7 S,, = specific gravity of water = 1.00 .. page A-6 4 And p of H,, under H20 = 62.34(13-57 - 1 .00) = 784 lb/ft3 / AP = = o.454A/im 12 X 144 6. d\ = 4.026 ............. ................... page B-16 do 2.00 7 cfi- 4.026 '4^7 - 8. C = 0.625 ............ ................... page A-19 9 Q = 236 x (2.0)* x 0.625 /o'.454 V 62.34 Q = 50.4 V Ahm ___calibration constant Solution -- (b): 10. Q = 50.4V A/im = 50.4V 4-4 = 106 11. M = 1.1 .................................. page A-3 ^ _ 50.6 x 106 x 62.34 12. 4.026 X 1.1 R, = 75 500 or 7.55 x ro4 i3- C = 0.625 is correct for Re = 7.55 x 104, per page A-19; therefore, the flow rate through the pipe is 106 gallons per minute. 14 When the C factor on page A-19 is incorrect, for the Reynolds number based on calculated flow, it must be adjusted until reasonable agree ment is reached by repeating Steps 9, 10, and 12. Example 4-24.. .Laminar Flow Inflow problems where the viscosity is high, calculate the Reynolds number to determine the type of flow. Given: SAE 10 Lube Oil at 90 F is flowing through a 3-inch Schedule 40 pipe and produces 0.4 psi pres sure differential between the flange taps of a 2.15-inch I. D. square edged orifice. Find: The flow rate in gallons per minute. Solution: 1. Q = 2360^0 CyjfAP ....... page 3-5 or 3-15 5-b Qp dp ........ page 3-2 or 3-8 2. p ~ 38. suspect laminar flow; page At3 3. di = 3.068 ......................................page B-16 ' d0 di 2.15 3.068 = 0.70 5 C = 0.8 ............... /page A-19; assumed value (based on laminar flow 6. S = 0.876 at 60 F S = 0.87 at 90 F .......................... page A-7 .......................... page A-7 7 p = 62.4 x 0.87 = 54.3 ................ page-A-7 8 Q = i36xi.i5ixo.8.T^=75 9 3.068 X 38 ,68 10 C = 0.92 for Rt = 1768 .............. page A-19 Since the assumed C value of 0.8 is not cor rect, it must be adjusted by repeating Steps /, 8, 9, and 10. 11. C= O.91 ........................ assumed; page A-19 12. Q = 236 x 2.152 x O.91 = 85-3 13 50.6 x 85.3 x 54-3 2010 3.068 X 38 14. C = 0.91 for Re = 2010 ................ page A-19 Since C = 0.91 is correct for the flow, the flow through the meter is 85.3 gallons per minute. ' 4-16.CHAPTER 4 -- EXAMPIES Of FlOW PROBLEMSCRANE Application of Hydraulic Radius to Flow Problems Example 4-25.. .Rectangular Duct Given: A rectangular concrete overflow aqueduct, 25 feet high and 16.5 feet wide, has an absolute roughness (e) of 0.01 foot. Find: The discharge rate in cubic feet per second when the liquid in the reservoir has reached the maximum height indicated in the above sketch. Assume the average tem perature of the water is 60 F. Solution: V1. q = 0.0438 cf2 K + Ka Then, resistance of entrance and exit, Ke = 1.0 + 0.5 = 1.5 .page 3-4 where; Ke = resistance of entrance and exit Ka = resistance of aqueduct To determine the flow rate, calculate the equivalent diameters for actual flow area. a = , therefore, d? = -- 4X A = ^-, therefore, D = A/-^- 4 \ TT To determine the friction factor from the Moody diagram, an equivalent diameter four times the hydraulic radius is used; refer to page 3-5. hydraulic radius = cross sectional flow area wetted perimeter _ qp R, = 22 700^dfi ,, ......................... page 3-2 2. cP = = 4_X.25X 16.5 X 144 =7?6qo 7T 7T D 4 x 25 X 16.5 22.Q 4. Assuming a sharp edged entrance, K = O.J ..................page A-26 Assuming a sharp edged exit to atmosphere, ^ = 1 - ..................ppaaggee AA--2266 5 Hydraulic radius = --X . = 4-97 ft J 2 (16.5 + 25) 6. Equivalent diameter, d = 4 x 4-97 x 12 d = 23Q in. 7 Relative roughness, t/D = 0.0005 ..pageA-23 8. f -- nr*it /fully turbulent flow 0-01' ..............................{assumed; page A-23 200 9- q = 0.0438 x 75 600 0.017 x 1000 1-5 + 22.q q - 31 300 . 10. Calculate Re and check, / = 0.017 for 31 300.cfs flow. 11. p = 62.34 ......................page A-6 12. p~ 1.1 ...................... page A-3 _ 22 700 x 31 300 X 62.34 13 ` 239 x 1.1 .Rj = 168 400 000 or 1.684 x 108 14. /= 0.017 .......... for calculated Re-, page A-24 i}. Since the friction factor assumed in Step 8 and that determined in Step 14 are in agree ment, the discharge flow will be 31 300 cfs. 16. If the assumed friction factor and the friction factor based on the calculated Reynolds num ber were not in reasonable agreement, the former should be adjusted and calculations repeated until reasonable agreement is reached. CRANE CHAPTER 4-- EXAMPLES OP ROW PROBLEMS Application of Hydraulic Radius to Flow Problems -- continued 4-17 Example 4-26.. .Pipe Partially Filled With Flowing Water Given: A cast iron water pipe is two-thirds full of flowing water (6o F). The pipe oas an inside diameter of 24 inches and a slope of /g-mch per foot. Note the sketch that follows. Find: The flow rate in gallons per minute. Solution: I. Q= 19.65 ........................page 3-4 To determine the flow rate in a partially full pipe, calculate the equivalent pipe diameters for the actual flow area. . a= 4 therefore, cf* = * A = ^-, therefore, D = ./4.-- 4 \w To determine the friction factor from the Moody diagram, an equivalent diameter four times the hydraulic radius is used; refer to page 3-5. cross sectional flow area hydraulic radius wetted perimeter R. = 50.6 dfi ...................... page 3-2 or 3-8 2. Depth of flowing water equals : -- (24) - 16 in. 3 . 3. Cos 4 --4 = 0.333 e = 7032' cc = 90 - 7032' = 1928' = 19.47 4. AreaC=^[l^^MZ)J Areac.^(i^).,,5il, f. 6 = V r2 - 4* = V 122 - 16 = 11.31 in. 6. Area A = Area B = 14 (4 b) = (4 x 11.3 0 Area A or B = 22.6 in2 7. The cross sectional area of flow equals: A + B + C = 22.6 + 22.6 + 275 = 320.2 in2 8. d? 4a 4 x 320.2 : 408 4 X 320.2 T X 144 I.683 9. hL = Ah = 0` 7? = 0.0625 ft per ft 10. The wetted perimeter equals: //. Hydraulic radius = ~~~ - 6.98 in. 12. Equivalent diameter d = 4 x 6.98 = 27.92 in. n- Relative roughness = 0.000 36___page A-23 14. / = 0.0155 'assuming fully turbu lent flow; page A-23 If. rQ, iq.6, 5 X 408o A /0--.-0--6--2--5 -X---1--.-6-83 \ 0.0155 x 1 Q = 20 qoo 16. Calculate the Reynolds number to check the friction factor assumed in Step 14. 17. . p * 62.34 .................. .-..................... page A-6 18. ju <*-i.i ..........................................page A-3 IQ, n ~ 50.6 x 20 900 x 62.34 y 27.92 x 1.1 R, = 2 150 000 or 2.15 x 10 20. / = 0.0155 .......................................... pageA-24 21. Since the friction factor assumed in Step 14 and that determined in Step 20 are in agree ment, the flow rate will be 20 900 gpm. 22. If the assumed friction factor, and the fric tion factor based on the calculated Reynolds number, were not in reasonable agreement, the former should be adjusted and the calculations repeated until reasonable agreement is reached. 4*18 -^iafiaaaw-'~ ' SfiBsbKfiM CHAPTER 4 - EXAMPLES OF FLOW FROSLEMS Determination of Boiler Capacity uau< CRANE ExampU 4-27 Given: A steam boiler operating at 300 psia saturated steam has a maximum capacity of 100,000 pounds per hour. Find: The boiler capacity in both kilo Btu per hour and in boiler horsepower. ' Solutions: Kile Btu per Hour: 1. ,, .. W(h, - h,) Boiler capacity----------------------- .................. page B-8 1000 2. h, - total heat of steam h, * iio2.8 Btu/lb .................. . page A-15 3- hf - heat of liquid hf - 393.8 Btu/lb .................. .page A-15 Boiler capacity 100000(1202.8-393.8) 4 = 80 900 kilo Btu/hr BolUr Horitpowtri 5 Boiler horsepower = ------------ 970.3 x 34.5 6. For values of h, and hf, see Steps 2 and }- - 7 Booiler .horsepower 100000(1202.8-393.8) =--------------- 1--- 970.3 x 34.5 Physical Properties of Fluids and Flow Characteristics of Valves, Fittings, and Pipe APPENDIX A 'The physical properties of many commonly used fluids are required for the solution of flow problems. These properties, compiled from many varied refer ence sources, are presented in this appendix. The convenience of a condensed presentation of these data will be readily apparent. . . Most texts on the subject of fluid mechanics cover in detail the flow through pipe, but the flow character istics of valves and fittings are given little, if any, attention, probably because the information has not been available. A means of estimating the re sistance coefficients for valves, deviating in minor detail from the standard forms for which the coeffi cients are known, is presented in Chapter %. The Y net expansion factors for discharge of compres sible fluids from piping systems, which are presented here for the first time, provide means for a greatly simplified solution of a heretofore complex problem. V5.11 11-"- A-2 dtit APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Viscosity of Steam14 ffia ' to tm 1 Example: Viscosity of 600 psig, 850 F steam is 0.029 centipoise. Adapted from: Philip J. Potter -- Steam Power Plants, Copyright 1949, The Ronald Press Company. CRANE APPENDIX A -- PHYSICAL PROPERTIES Of FLUIDS-AND Flow CHARACTERISTICS OP VALVES. PITTINGS, AND PIPE Viscosity of Water and Liquid Petroleum Products8'12,23 A-ff 1. Ethane (CiHe) 2. Propane (CjHs) 3. Butan* (CH,0) 4. Natural Gasoline 5. Gasoline 6. Water 7. Kerosene 8. Distillate 9. 48 Deg. API Crude 10. 40 Deg. API Crude 11. 35.6 Deg. API Crude 12. 32.6 Deg. API Crude 13. Salt Creek Crude 14. Fuel 3 (Max.) 15. Fuel 5 (Min.) 16. SAE 10 Lube (100 V.l.) 17. SAE 30 Lube (100 V.l.) 18. Fuel 5 (Max.) or Fuel 6 (Min.) 19. SAE 70 Lube (100 V.l.) . 20. Bunker C Fuel (Max.) and M.C. Residuum 21. Asphalt Data extracted in part by permission from the Oil and Gas Journal. Example: The viscosity of water at 125 F is 0.52 centipoise (Curve No. 6). A-4 usi3*i APPENDIX A -- PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE Viscosity of Various Liquids5'8'11 CRANE m n m inn m n in m m iin 1. Carbon Dioxide..C02 2. Ammonia........NHj 3. Methyl Chloride. .CH3Cf 4. Sulphur Dioxide..SO2 5. Freon 12..............F-12 6. Freon 114...... .F-l 14 7. Freon 11............. .F-l 1 8. Freon 113.............F-113 t - Temperature, in Degrees Fahrenheit 9. Ethyl Alcohol 10. Isopropyl Alcohol 11. 20% Sulphuric Acid........... 20% H2S04 12. Dowtherm E 13. Dowtherm A 14. 20% Sodium Hydroxide. .20% NaOH 15. Mercury 16. 10% Sodium Chloride Brine... 10% NaCI 17. 20% Sodium Chloride Brine.. .20% NaCI 18. 10% Calcium Chloride Brine.. 10% CaCI2 19. 20% Calcium Chloride Brine. .20% CaCI2 Example: The viscosity of am monia at 40 F is 0.14 centipoise. CRANE APPENDIX A - PHYSICAL PtOKHTiefO? ANP H.O'MCkAKACTailSTICS Of VALVES. FITTINGS, AND Viscosity of Gases and Vapors A- The curves for hydrocarbon vapors and natural gases in the chart at the upper right are taken from Maxwell15; the curves for all other gases in the chart are based upon Sutherland's formula, as follows: Q-555 To + h Ho ,0-555 T + where: jx = viscosity, in centipoise at temperature T. ' Ho = viscosity, in centipoise at temperature To T -- absolute temperature, in de grees Rankine (460 + deg. F) for which viscosity is desired. To = absolute temperature, in de grees Rankine, for which vis cosity is known. C = Sutherland's constant. Note: The variation of viscosity with pressure is small for most gases. For gases given on this page, the correction of viscosity for pressure is less than 10 per cent for pressures up to 500 pounds per square inch. Fluid O, Air Nj CO, CO so, NH, H, Approximate Values of "C" 127 120 111 240 118 416' 370 72 Upper chart example: The viscosity of sulphur dioxide gas (SO2) at 200 F is 0.016 centipoise. Lower chart example: The viscosity of carbon dioxide gas (C02) at about 80 F is 0.015 centipoise.- Viscosity of Various Gases HYDRO CARBON VAPOR ANO NATURAL GASES t - Temperature, in Degrees Fahrenheit Viscosity of Refrigerant Vapors11 (safuratsd and suptrhsatsd vapors) -40 0 40 80 120 160 t - Temperature, in Degrees Fahrenheit 200 240 A-6 APPENDIX A-PHYSICAL PROPERTIES OF FlUIDS AND FLOW CHARACTERISTICS OF VAIVES, FITTINGS, AND PIPE Physical Properties of Water CRANE Temperature of Water t Degrees Fahrenheit 32 40 50 60 70 80 90 100 no 120 130 140 150 160 170 180 190 200 210 212 220 240 260 280 300 350 400 450 500 550 600 700 Saturation Pressure P' Pounds per Square Inch Absolute .08854 .12170 .17811 .2563 .3631 .5069 .6982 .9492 1.2748 1.6924 2.2225 2.8886 3.718 4.741 5.992 7.510 9.339 11.526 14.123 14.696 17.186 24.969 35.429 49.203 67.013 134.63 247.31 422.6 680.8 1045.2 1542.9 3093.7 Specific Volume V Cubic Feet Per Pound .01602 .01602 .01603 .01604 .01606 .01608 .01610 .01613 .01617 .01620 .01625 .01629 .01634 .01639 .01645 .01651 .01657 .01663 .01670 .01672 .01677 .01692 .01709 .01726 .01745 .01799 .01864 .0194 .0204 .0218 .0236 .0369 Weight Density P Pounds per Cubic Foot 62.42 62.42 62.38 62.34 62.27 62.19 62.11 62.00 61.84 61.73 61.54 61.39 61.20 ` 61.01 60.79 60.57 60.35 60.13 59.88 59.81 59.63 59.10 58.51 57.94 57.31 55.59 -53.65 51.55 49.02 45.87 42.37 27.10 Weight Pounds Per Gallon 8.345 8.345 8.340 8.334 8.325 8.314 8.303 8.289 8.267 8.253 8.227 8.207 8.182 8.156 8.127 8.098 8.068 8.039 8.005 7.996 7.972 7.901 7.822 7.746 7.662 7.432 7.172 6.892 6.553 6.132 5.664 3.623 Specific gravity of water at 60 F= 1.00 Weight per gallon is based on 7.48 gallons per cubic foot. All data on volume and pressure abstracted from Keenan and Keyes' Steam Tables (1936). CRANE APPENDIX A - PHYSICAL PHOPEHTIES OF PLUIDS AND PLOW CHARACTERISTICS OP VALVES, PITTINOS. AND PIPE Specific Gravity-Temperature Relationship for Petroleum Oils12 (Reproduced by permission from the Oil and Gas Journal) A-7 C:Hs*Ethan CjHj=Propar /C-iHjo--Jjobulan# C(Hio=Suton iCiHi]--Isapentan* Example: The specific gravity of an oil at 60 F is 0.85 The specific gravity at 100 F = 0.83. 300 400 500 600 t --Temperature, in Degrees Fahrenheit 1000 To find the weight density of a petroleum oil at its flowing temperature when the specific gravity at 6o F/6o F is known, multiply th.e specific gravity of the oil at flowing temperature (see chart above) by 62.4, the density of water at 60 F. Weight Density and Specific Gravity* of Various Liquids Liquid Temp. Weight Specific Density Gravity /p FDaehgr.. LCbus.. Fpte:r S Acetone Ammonia, Saturated Benzene Brine, 10% Ca Cl Brine, 10% Na Cl Bunkers C Fuel Max. Carbon Disulphide Distillate Fuel 3 Max. Fuel 5 Min. Fuel 5 Max. Fuel 6 Min. Gasoline Gasoline, Natural Kerosene M. C. Residuum 60 10 32 32 32 60 32 60 60 60 60 60 60 60 60 60 49.4 40.9 56.1 68.05 67.24 63.25 80.6 52.99 56.02 60.23 61.92 61.92 46.81 42.42 50.85 58.32 0.792 1.014 0.850 0.898 0.966 0.993 0.993 0.751 0.680 0.815 0.935 Liquid Mercury Mercury Mercury Mercury Mercury Milk Olive Oil Pentane SAE 10 Lube| SAE 30 Lubet SAE 70 Lubef Salt Creek Crude 32.6 API Crude 35.6 API Crude 40 API Crude 48 API Crude Temp. Weight Specific . Density Gravity `Liquid at 60 F referred 1 FDaehgr.. 20 40 60 80 p5 LCbus.. Fpte.r 849.74 -------------- 848.03 846.32 13'570 844.62 to water at 60 F. fMilk has a weight density or o4.Z to o4.o. tlOO Viscosity Index. 100 842.93 `59 t 57.3 09*j*9 59 38.9 o!624 Values in the table at the left were taken from Smithsonian 60 54.64 0.876 Physical 'fables, 60 60 56.02 57.12 9?f 60 52.56 0^843 Mark's Engineers' Handbook, and 12Nel- 60 53.77 0.862 son's Petroleum Re- 60 60 52.81 51.45 2U.oZ? 'finery Engineering. 60 49.16 0.788 It nm e I f i1 1 1 1B1 1 1 1 B1 II8 1 II1 1 8 8 1 1 1 t f r f H A - 8APPENDIX A-PHVSICAL PROPERTIES OF FLUIDS AND FlOW CHARACTERISTICS Of VALVES, FITTINGS. AND PIPE CRANE Physical Properties of Gases18 c,, = specific heat at constant pressure c,-- specific heat at constant volume Name of Gas, Chemical Approx. Formula Molecu or lar Symbol Weight M Weight Density, Pounds per Cubic Foot* /> Specific Indi Gravity vidual Rela Gas tive Constant To Air <s R Specific Heat Per Pound at Room Temperature Cp CV Heat Capacity . Per Cubic Foot at Atmospheric Pressure and 68 F v C9 Acetylene Air Ammonia Argon Carbon Dioxide Carbon Monoxide Ethylene Helium Hydrochloric Acid Hydrogen Methane Methyl Chloride Nitrogen Nitric Oxide Nitrous Oxide Oxygen Sulphur Dioxide O--H* NH, A CO, CO c,h4 He HC1 H, CH, CH,C1 N, NO N,G o, SO, 26.0 29.0 17.0 40.0 44.0 28.0 28.0 4.0 36.5 2.0 16.0 50.5 28.0 30.0 44.0 32.0 64.0 .06754 .07528 .04420 .1037 .1142 .07269 .0728 .01039 .09460 .005234 .04163 .1309 .07274 .07788 .1143 .08305 .1663 .897 1.000 .587 1.377 1.516 .965 .967 .138 1.256 .0695 .553 1.738 .966 1.034 1.518 1.103 2.208 59.4 53.3 90.8 38.7 35.1 55.2 55.1 386. 42.4 767. 96.4 30.6 55.2 51.5 35.1 48.3 24.1 .350 .241 .523 .124 .205 .243 .40 1.25 .191 3.42 .593 .24 .247 .231 .221 .217 .154 .2737 .1725 .4064 .0743 .1599 .1721 .3292 .754 .1365 2.435 .4692 .2006 .1761 .1648 .1759 .1549 .1230 'Weight density values are at atmospheric pressure and 68 F. For vali -.s at 60 F, multiply by 1.0154. .0236 .0181 .0231 .0129 .0234 .0177 .0291 .0130 .0181 .0179 .0247 .0314 .0179 .0180 .0253 .0180 .0256 .0185 .0130 .0179 .0077 .0183 .0125 .0240 .0078 .0129 .0127 .0195 .0263 .0128 .0128 .0201 .0129 .0204 k equal to Cj/C, 1.28 1.40 1.29 1.67 1.28 1.41 1.22 1.66 1.40 1.40 1.26 1.20 1.40 1.40 1.26 1.40 1.25 Volumetric Composition and Specific Gravity of Gaseous Fuels18 Type of Gas Chemical Composition Percent by Volume Hydro gen Carbon Mon oxide Paraffin Hydrocarbons Meth Eth ane ane Illuminants Ethyl Ben ene zene Oxy gen Specific Gravity Relative Nitro Carbon to Air gen Diox ide Natural Gas, Pittsburgh Producer Gas from Bituminous Coal Blast Furnace Gas Blue Water Gas from Coke Carbureted Water Gas Coal Gas (Cont. Vertical Retorts) Coke-Oven Gas Refinery Oil Gas (Vapor Phase) Oil Gas, Pacific Coast 14.0 1.0 47.3 40.5 54.5 46.5 13.1 48.6 27.0 27.5 37.0 34.0 10.9 6.3 1.2 12.7 83.4 15.8 3.0 1.3 10.2 24.2 32.1 23.3 26.3 21.7 6.1 1.5 3.5 39.6 2.7 2.8 1.3 0.5 1.1 0.8 0.6 50.9 4.5 60.0 11.5 0.7 8.3 5.4 0.5 2.9 3.0 0.2 4.4 3.0 0.8 8.1 2.2 1.0 0.1 0.3 3.6 4.7 0.61 0.86 1.02 0.57 0.63 0.42 0.44 0.89 0.47 Data on this page reproduced by permission from Mechanical Engineers' Handbook by L. S. Marks. Copyright, May, 1954; McGraw-Hill Book Company. Inc. CRANE Affecoc A-WWSICAL ttOPHtTIES Of FLUIDS AND how CHAHACTEWSTICS or VALVES, flTTINGS, AND PIPE Steam --1 Values of k Ratio of Specific Heat at Constant Pressure to Specific Heat at Constant Volume k = Co/e* A-9 For small changes in pressure (or volume) along an isentropic, po* = constant Reprinted from "Thermodynamic Properties of Steam" by J, H. Keenan and F. G. Keyes, 1936 edition, by permission of the publishers, John Wiley & Sons, Inc. ***'>* f a A-10 i APPENDIX A-PHYSICAL PROPERTIES Of FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Weight Density and Specific Volume Of Gases and Vapors The chart on page A-i 1 is based on the formula: , _ 144 P' MP' 2.70 PS, p ~ RT ~ >0.72 T ~ T where: P' = 14.7 + P Problem: What is the density of dry CH, if the temperature is 100 F and the gauge pressure is 15 pounds per square inch? Solution: Refer to the table on page A-8 for molecular weight, specific gravity, or individual gas constant. Connect 96.4 of the R scale with 100 on the temper ature scale, t, and mark the intersection with the index scale. Connect this point with 1 y on the pressure scale, P. Read the answer, 0.08 pounds per cubic foot, on the weight density scale p. Air Temp. Deg F. Weight Density of Air Weight Density of Air, in Pounds per Cubic Foot For Gauge Pressures Indicated (Based on an atmospheric pressure of 14.6% and a molecular weight of 28.97) 0 5 10 . 20 30 40 50 60 70 80 90 100 110 120 130 140 150 psi psi psi psi psi ' psi psi psi psi psi psi psi psi psi psi psi psi 30 II .0811 .1087 .1363 .1915 .247 40 .0795 .1065 .1335 .1876 .242 50 .0782 .1048 .1314 .1846 .238 60 .0764 .1024 .1284 .1804 .232 70 II .0750 .1005 .1260 .1770 .228 .302 .295 .291 .284 .279 .357 .350 .344 .336 .330 .412 .404 .397 .388 .381 .467 .458 .451 .440 .432 .522 .512 .504 .492 .483 .578 .566 .557 .544 .534 .633 .620 .610 .5% .585 .688 .674 .663 .648 .636 .743 .728 .717 .700 .687 .798 .782 .770 .752 .738 .853 .836 .823 .804 .789 .909 .890 .876 .856 .840 80 .0736 .0986 .1236 .1737 .224 .274 .324 .374 .424 .474 .524 .574 .624 .674 .724 .774 .824 90 .0722 .0968 .1214 .1705 .220 .269 .318 .367 .416 .465 .515 .564 .613 .662 .711 .760 .809 100 .0709 .0951 .1192 .1675 .216 .264 .312 .361 .409 .457 .505 .554 .602 .650 .698 .747 .795 110 .0697 .0934 .1171 .1645 .212 .259 .307 .354 .402 .449 .497 .544 .591 .639 .686 .734 .781 120 .0685 .0918 .1151 .1617 .208 .255 .302 348 .395 .441 .488 .535 .581 .628 .674 .721 .768 130 .0673 .0902 .1131 .1590 .205 .251 .2% .342 .388 .434 .480 .525 .571 .617 .663 .709 .755 140 .0662 .0887 .1113 .1563 .201 .246 .291 .337 .382 .427 .472 .517 .562 .607 .652 .697 .742 150 .0651 .0873 .1094 .1537 .1981 .242 .287 .331 .375 .420 .464 .508 .553 .597 .641 .686 .730 175 .0626 .0834 .1051 .1477 .1903 .233 .275 .318 .361 .403 .446 .488 .531 .573 .616 .659 .701 200 .0602 .0807 .1011 .1421 .1831 .224 .265 .306 .347 .388 .429 .470 .511 .552 .593 .634 .675 I 5i\ i \\I1i 225 .0580 .0777 .0974 .1369 .1764 .216 .255 .295 .334 .374 .413 .453 .492 .531 .571 .610 .650 250 .0559 .0750 .0940 .1321 .1702 .208 .246 .284 .322 .361 .399 .437 .475 .513 .551 .589 .627 275 .0540 .0724 .0908 .1276 .1644 .201 .238 .275 .311 .348 .385 .422 .459 .495 .532 .569 .606 300 .0523 .0700 .0878 .1234 .1590 .1945 .230 .266 .301 .337 .372 ' ~408 .443 .479 .515 .550 .586 350 .0490 .0657 .0824 .1158 .1491 .1825 .216 .249 .283 .316 .349 .383 .416 .449 .483 .516 .550 400 .0462 .0619 .0776 .1090 .1405 .1719 .203 .235 .266 .298 .329 .360 .392 .423 .455 .486 .518 450 .0436 .0585 .0733 .1030 .1327 .1624 .1921 .222 .252 .281 .311 .341 .370 .400 .430 .459 .489 500 .0414 .0555 .0695 .0977 .1258 .1540 .1821 .210 .238 .267 .295 .323 .351 .379 .407 .436 .464 550 .0393 .0527 .0661 .0928 .1196 .1464 .1731 .1999 .227 .253 .280 .307 .334 .360 .387 .414 .441 600 .0375 .0502 .0630 .0885 .1140 .1395 .1649 .1904 .216 .241 .267 .292 .318 .343 .369 .394 .420 175 200 225 250 300 400 500 600 700 800 900 1000 psi psi psi psi psi psi psi psi psi psi psi psi 30 40 50 60 70 80 90 100 110 120 130 140 150 175 200 225 250 275 300 350 400 450 500 550 600 1.047 1.026 1.009 .986 .968 .950 .932 .916 .900 .884 .869 .855 .841 .807 .777 .749 .722 .698 .675 .633 .596 .563 .534 .508 .484 1.185 1.161 1.142 1.116 1.095 1.075 1.055 1.036 1.018 1.001 .984 .967 .951 .914 .879 .847 .817 .790 .764 .716 .675 .638 .604 .575 .547 1.323 1.296 1.275 1.246 1.223 1.200 1.178 1.157 1.137 1.117 1.098 1.080 1.062 1.020 .982 .946 .913 .881 .852 .800 .753 .712 .675 .641 .611 1.460 1.431 1.408 1.376 1.350 1.325 1.301 1.278 1.255 1.234 1.213 1.193 1.173 1.127 1.084 1.044 1.088 .973 .941 .883 .832 .786 .745 .708 .675 1.736 1.702 1.674 1.636 1.605 1.575 1.547 1.519 1.492 1.467 1.442 1.418 1.395 1.340 1.289 1.242 1.198 1.157 1.119 1.050 .989 .934 .886 .842 .802 2.29 2.24 2.21 2.16 2.12 2.84 2.78 2.74 2.68 7.63 2.08 2.04 2.00 1.967 1.933 2.58 2.53 2.48 2.44 2.40 1.900 1.868 1.838 1.765 1.698 2.36 2.32 2.28 2.19 2.11 1.636 1.579 1.525 1.475 1.384 2.03 1.959 1.893 1.830 1.717 1.303 1.232 1.167 1.110 1.057 1.618 1.529 1.449 1.377 1.312 3.39 3.32 3.27 3.20 3.14 3.08 3.02 2.97 2.92 2.86 2.82 2.77 2.72 2.62 2.52 2.43 2.34 2.26 2.19 2.05 1.932 1.826 1.731 1.645 1.567 3.94 3.86 3.80 3.72 3.65 3.58 3.51 3.45 3.39 3.33 3.27 3.22 3.17 3.04 2.93 2.82 2.72 2.63 2.54 2.38 2.25 2.12 2.01 1.912 1.822 4.49 4.40 4.33 4.24 4.16 4.08 4.00 3.93 3.86 3.80 3.73 3.67 3.61 3.47 3.34 3.21 3.10 3.00 2.90 2.72 2.56 2.42 2.29 2.18 2.08 5.05 4.95 4.87 4.76 4.67 4.58 4.50 4.42 4.34 4.26 4.19 4.12 4.05 3.89 3.75 3.61 3.48 3.36 3.25 3.05 2.87 2.72 2.58 2.45 2.33 5.60 Air Deniity Table 5.49 5.40 The table at the left is cal- 5.28 5.18 5.08 culated for the perfect gas law shown at the top of the 4.99 page. Correction for super 4.90 compressibility, the devia 4.81 4.73 tion from the perfect gas 4.65 law, would be less than 4.57 three percent and has not 4.50 4.32 been applied. 4.16 4.00 3.86 The weight density of gases other than air can be deter 3.73 mined from this table by 3.61 3.39 multiplying the density 3.19 listed for air by the specific 3.01 gravity of the gas relative 2.86 2.72 to air, as listed in the tables 2.59 on page A-8. i CRANE APPENDIX A - PHYSICAL PKOfEHTIB OF HU1PS AND FLOW CHARACTERISTICS Of VALVES. FITTINGS, AND PIPE A-n M R Sg 10- 150- 1--0.35 -0.4 -0.5 15100' 90 -0.6 80-- 20- -0.7 70-r -0.8 - O 60- -0.9 cn _ CCD3 CD j, 30--" * - I 50 -I - -1.0 a<>3. I 4040- -1.5 5030-L Weight Density and Specific Volume Of Gases and Vapors -- continued Index X pv .015--1 >60 .02- 50 3--40 .03 -30 .04-: P r-o .057fr20 .06 .07 .08 .09 .10o O .2- CL. -10 I -9 "8 5 -7 a> -6 -5 o -4 .3-q Oa> J-3 i -4"t .*2a>? S- o xs 1 .6- i a .7 .8 .9 1- -1 -.9 -.8 -.7 -.6 F-io t F--20 r-200 651 +"1_80 x-z -160 | -30 Mo | 600--I--140 CO 5 Ca>L aa> 50 -100 --60 O 550--I-- -80 <c . I +-60 2 8. -70 E -80 i -90 501 -40 490--30 -100 i a* h-150 -.5 I--200 1-.4 Pressure, in Pounds per Square Inch Gauge t--2.0 60- r70 78 20--L1 2.7 For application of chart, refer to iho explanation on tho preceding page. Molecular weight, specific gravity, and individual constantt for various gases are given on page A-8. >300 M00 ggDgBBflflflBgcBBBflflonnnnflTi I -frt A-12 APPENDIX a-PHYSICAL PROPERTIES OF FLUIDS AND Flow CHARACTERISTICS OF VAIVES, FITTINGS, AND PIPE Properties of Saturated Steam1" CRANE i I I% 1 * ; . - i j , >i - s a Absolute Pressure Lbs. per Sq. In. Inches of Hg ?' 0.20 0.25 0.30 0.35 0.40 0.45 0.41 0.51 0.61 0.71 0.81 0.92 0.50 0.60 0.70 0.80 0.90 1.0 1.2 1.4 1.6 1.8 2.0 2.2 ' 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 11.0 12.0 13.0 14.0 1.02 1.22 1.43 1.63 1.83 2.04 2.44 2.85 3.26 3.66 4.07 4.48 4.89 5.29 5.70 6.11 7.13 8.14 9.16 10.18 11.20 12.22 13.23 14.25 15.27 16.29 17.31 18.32 19.34 20.36 22.40 24.43 26.47 28.50 Vacuum Inches of Hg 29.51 29.41 29.31 29.21 29.11 29.00 28.90 28.70 28.49 28.29 28.09 27.88 27.48 27.07 26.66 26.26 25.85 25.44 25.03 24.63 24.22 23.81 22.79 21.78 20.76 .19.74 18.72 17.70 16.69 15.67 14.65 13.63 12.61 11.60 10.58 9.56 7.52 5.49 3.45 1.42 Temperature t Degrees F. 53.14 59.30 64.47 68.93 72.86 76.38 79.58 85.21 90.08 94.38 98.24 101.74 107.92 113.26 117.99 122.23 126.08 129.62 132.89 135.94 138.79 141.48 147.57 152.97 157.83 162.24 166.30 170.06 173.56 176.85 179.94 182.86 185.64 188.28 190.80 193.21 197.75 201.% 205.88 209.56 Heat of the Liquid Btu/lb. 21.21 27.36 32.52 36.97 40.89 44.41 47.60 53.21 58.07 62.36 66.21 69.70 75.87 .81.20 85.91 90.14 93.99 97.52 100.79 103.83 106.68 109.37 115.46 120.86 125.71 130.13 134.19 137.96 141.47 144.76 147.86 150.79 153.57 156.22 158.75 161.17 165.73 169.96 173.91 177.61 Latent Heat of Evaporation Btu/lb. 1063.8 1060.3 1057.4 1054.9 1052.7 1050.7 1048.8 1045.7 1042.9 1040.4 1038.3 1036.3 1032.7 1029.6 1026.9 1024.5 1022.2 1020.2 1018.3 1016.5 1014.8 1013.2 1009.6 1006.4 1003.6 1001.0 998.5 996.2 994.1 992.1 990.2 988.5 986.8 985.2 983.6 982.1 979.3 976.6 "974.2 971.9 Total Heat of Steam K Btu/lb. 1085.0 1087.7 1090.0 1091.9 1093.6 1095.1 10%.4 1098.9 1101.0 1102.8 1104.5 1106.0 1108.6 1110.8 1112.8 1114.6 1116.2 1117.7 1119.1 1120.3 1121.5 1122.6 1125.1 1127.3 1129.3 1131.1 1132.7 1134.2 1135.6 1136.9 1138.1 1139.3 1140.4 1141.4 1142.3 1143.3 1145.0 1146.6 1148.1 1149.5 . Specific Volume V Cu. ft. per lb. 1526.0 1235.3 1039.5 898.5 791.9 708.5 641.4 540.0 466.9 411.7 368.4 333.6 280.9 243.0 214.3 191.8 173.73 158.85 146.38 135.78 126.65 118.71 102.72 90.63 81.16 73.52 67.24 61.98 57.50 53.64 50.29 47.34 44.73 42.40 40.31 38.42 35.14 32.40 30.06 28.04 Pressure Lbs. per Sq. In. Absolute , P' Gage P 14.696 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0 0.0 0.3 1.3 2.3 3.3 4.3 5.3 ' 6.3 7.3 8.3 9.3 10.3 11.3 12.3 13.3 14.3 15.3 16.3 17.3 18.3 19.3 Temperature t Degrees F. 212.00 213.03 216.32 219.44 222.41 225.24 ' 227.% 230.57 233.07 235.49 237.82 240.07 242.25 244.36 246.41 248.40 250.33 252.22 254.05 255.84 257.58 Heat of the Liquid Btu/lb. 180.07 181.11 184.42 187.56 190.56 193.42 1%.16 198.79 201.33 203.78 206.14 '208.42 210.62 212.75 214.83 216.86 218.82 220.73 222.59 224.41 226.18 Latent Heat of Evaporation Btu/lb. 970.3 %9.7 %7.6 965.5 963.6 961.9 %0.1 958.4 956.8 955.2 953.7 952.1 950.7 949.3 947.9 946.5 945.3 944.0 942.8 941.6 940.3 * Abstracted from Thermodynamic Properties of Steam by J. H. Keenan and F.G.Keyes, I936Edition, by permission of the publishers, John Wiley & Sons, inc. Total Heat of Steam .K Btu/lb. 1150.4 1150.8 1152.0 1153.1 1154.2 1155.3 1156.3 1157.2 1158.1 1159.0 1159.8 1160.6 1161.3 1162.0 1162.7 1163.4 1164.1 1164.7 1165.4 1166.0 1166.5 Specific Volume V Cu. ft. per lb. 26.80 26.29 24.75 23.39 22.17 21.08 20.089 19.192 18.375 17.627 16.938 16.303 15.715 15.170 14.663 14.189 13.746 13.330 12.940 12.572 12.226 (confirmed on roenexfpcgej fi l-B-B-B-B BBBBBBfifilBBBBB $f CRANE APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE A- 13 Properties of Saturated Steam -- continued Pressure Lbs. per Sq. In. Absolute ?' Gage P 35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0 60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0 80.0 81.0 82.0 83.0 84.0 85.0 86.0 87.0 88.0 89.0 90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 99.0 100.0 101.0 102.0 103.0 104.0 105.0 106.0 107.0 108.0 109.0 20.3 21.3 22.3 23.3 24.3 25.3 26.3 27.3 28.3 29.3 30.3 31.3 32.3 33.3 34.3 35.3 36.3 37.3 38.3 39.3 40.3 41.3 42.3 43.3 44.3 45.3 46.3 47.3 48.3 49.3 50.3 51.3 52.3 53.3 54.3 55.3 56.3 57.3 58.3 59.3 60.3 61.3 62.3 63.3 64.3 65.3 66.3 67.3 68.3 69.3 70.3 71.3 72.3 73.3 74.3 75.3 76.3 77.3 78.3 79.3 80.3 81.3 82.3 83.3 84.3 85.3 86.3 87.3 88.3 89.3 90.3 91.3 92.3 93.3 94.3 Temperature t Degrees F. 259.28 260.95 262.57 264.16 265.72 267.25 268.74 270.21 271.64 273.05 274.44 275.80 277.13 278.45 279.74 281.01 282.26 283.49 284.70 285.90 287.07 288.23 289.37 290.50 291.61 292.71 293.79 294.85 295.90 296.94 297.97 298.99 299.99 300.98 301.% 302.92 303.88 304.83 305.76 306.68 307.60 308.50 309.40 310.29 311.16 312.03 312.89 313.74 314.59 315.42 316.25 317.07 317.88 318.68 319.48 . 320.27 321.06 321.83 322.60 323.36 324.12 324.87 325.61 326.35 327.08 327.81 328.53 329.25 329.% 330.66 331.36 332.05 332.74 333.42 334.10 Heat of the Liquid Btu/lb. 227.91 229.60 231.26 232.89 234.48 236.03 237.55 239.04 240.51 241.95 243.36 244.75 246.12 247.47 248.79 250.09 251.37 252.63 253.87 255.09 256.30 257.50 258.67 259.82 260.96 262.09 263.20 264.30 265.38 266.45 267.50 268.55 269.58 270.60 271.61 272.61 273.60 274.57 275.54 276.49 277.43 278.37 279.30 280.21 281.12 282.02 282.91 283.79 284.66 285.53 286.39 287.24 288.08 288.91 289.74 290.56 291.38 292.18 292.98 293.78 294.56 295.34 2%. 12 2%. 89 297.65 298.40 299.15 299.90 300.64 301.37 302.10 302.82 303.54 304.26 304.97 Latent Heat of Evaporation Btu/lb. 939.2 938.0 936.9 935.8 934.7 933.7 932.6 931.6 930.6 929.6 928.6 927.7 926.7 925.8 924.9 924.0 923.0 922.2 921.3 920.5 919.6 918.8 917.9 917.1 916.3 915.5 914.7 913.9 913.1 912.3 911.6 910.8 910.1 . 909.4 908.7 907.9 907.2 906.5 905.8 905.1 904.5 903.7 903.1 902.4 901.7 901.1 900.4 899.7 899.1 898.5 897.8 897.2 8%.5 895.9 895.3 894.7 894.1 893.5 892.9 892.3 891.7 891.1 890.5 889.9 889.4 888.8 888.2 887.6 887.1 886.5 886.0 885.4 884.9 884.3 883.7 Total Heat of Steam hg Btu/lb. 1167.1 1167.6 1168.2 1168.7 1169.2 1169.7 1170.2 1170.7 1171.1 1171.6 1172.0 1172.4 1172.9 1173.3 1173.7 1174.1 1174.4 1174.8 1175.2 1175.6 1175.9 1176.3 1176.6 1176.9 1177.3 1177.6 1177.9 1178.2 1178.5 1178.8 1179.1 1179.4 1179.7 1180.0 1180.3 1180.6 1180.8 1181.1 1181.3 1181.6 1181.9 1182.1 1182.4 1182.6 1182.8 1183.1 1183.3 1183.5 1183.8 1184.0 1184.2 1184.4 1184.6 1184.8 1185.1 1185.3 1185.5 1185.7 1185.9 1186.1 1186.2 1186.4 1186.6 1186.8 1187.0 1187.2 1187.4 1187.5 1187.7 1187.9 1188.1 1188.2 1188.4 1188.6 1188.7 < . Specific Volume V Cu. ft. per lb. 11.898 11.588 11.294 11.015 10.750 10.498 10.258 10.029 9.810 9.601 9.401 9.209 9.025 8.848 8.678 8.515 8.359 ` 8.208 8.062 7.922 7.787 7.656 7.529 7.407 7.289 7.175 7.064 6.957 6.853 6.752 6.655 6.560 6.468 6.378 6.291 6.206 6.124 6.044 5.%6 5.890 5.816 5.743 5.673 5.604 5.537 5.472 5.408 5.346 5.285 5.226 5.168 5.111 5.055 5.001 4.948 4.8% 4.845 4.7% 4.747 4.699 4.652 4.606 4.561 4.517 4.474 4.432 4.391 4.350 4.310 4.271 4.232 4.194 4.157 4.120 4.084 ? 9 I r :n u n n o D D B flm g iiiiiiiflB n fljj A.14 APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES. FITTINGS, AND PIPE CRAMP Properties of Saturated Steam -- continued Pressure Lbs. Per Sq. In. Temperature Heat of the Liquid Latent Heat of Evaporation Total Heat of Steam Absolute P' 110.0 111.0 112.0 113.0 114.0 115.0 116.0 117.0 118.0 119.0 120.0 121.0 122.0 123.0 124.0 125.0 126.0 127.0 128.0 129.0 130.0 131.0 132.0 133.0 134.0 135.0 136.0 137.0 138.0 139.0 140.0 141.0 142.0 143.0 144.0 145.0 146.0 147.0 148.0 149.0 150.0 152.0 154.0 156.0 158.0 160.0 162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0 180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0 200.0 205.0 210.0 215.0 220.0 225.0 230.0 235.0 240.0 245.0 - Gage P 95.3 96.3 97.3 98.3 99.3 100.3 101.3 102.3 103.3 104.3 105.3 106.3 107.3 108.3 109.3 110.3 111.3 112.3 113.3 114.3 115.3 116.3 117.3 118.3 119.3 120.3 121.3 122.3 123.3 124.3 125.3 126.3 127.3 128.3 129.3 130.3 131.3 132.3 133.3 134.3 135.3 137.3 139.3 141.3 143.3 145.3 147.3 149.3 151.3 153.3 155.3 157.3 159.3 161.3 163.3 165.3 167.3 169.3 171.3 173.3 175.3 177.3 179.3 181.3 183.3 185.3 190.3 195.3 200.3 205.3 210.3 215.3 220.3 225.3 230.3 t Degrees F. 334.77 335.44 336.11 336.77 337.42 338.07 338.72 339.36 339.99 340.62 341.25 341.88 342.50 343.11 343.72 344.33 344.94 345.54 346.13 346.73 347.32 347.90 348.48 349.06 349.64 350.21 350.78 351.35 351.91 352.47 353.02 353.57 354.12 354.67 355.21 355.76 356.29 356.83 357.36 357.89 358.42 359.46 360.49 361.52 362.53 363.53 364.53 365.51 366.48 367.45 368.41 369.35 370.29 371.22 372.14 373.06 373.96 374.86 375.75 376.64 377.51 378.38 379.24 380.10 380.95 381.79 383.86 385.90 387.89 389.86 391.79 393.68 395.54 397.37 399.18 Btu/lb. 305.66 306.37 307.06 307.75 308.43 309.11 309.79 310.46 311.12 311.78 312.44 313.10 313.75 314.40 315.04 315.68 316.31 316.94 317.57 318.19 318.81 319.43 320.04 320.65 321.25 321.85 322.45 323.05 323.64 324.23 324.82 325.40 325.98 326.56 327.13 327.70 328.27 328.83 329.39 329.95 330.51 331.61 332.70 333.79 334.86 335.93 336.98 338.02 339.05 340.07 341.09 342.10 343.10 344.09 345.06 346.03 347.00 347.96 348.92 349.86 350.79 351.72 352.64 353.55 354.46 355.36 357.58 359.77 361.91 364.02 366.09 368.13 370.14 372.12 374.08 Btu/lb. 883.2 882.6 882.1 881.6 881.1 880.6 880.0 879.5 879.0 878.4 877.9 877.4 876.9 876.4 875.9 875.4 874.9 874.4 873.9 873.4 872.9 872.5 872.0 871.5 871.0 870.6 870.1 869.6 869.1 868.7 868.2 867.7 867.2 866.7 866.3 865.8 865.3 864.9 864.5 864.0 ..... 863.6 862.7 - _ 861.8 860.9 860.0 859.2 858.3 857.5 856.6 855.7 854.9 854.1 853.3 852.4 851.6 850.8 850.0 849.2 848.4 847.6 846.8 846.1 845.3 844.5 843.7 843.0 841.1 839.2 837.4 835.6 833.8 832.0 830.3 828.5 826.8 K Btu/lb. 1188.9 1189.0 1189.2 1189.4 ' 1189.5 1189.7 1189.8 1190.0 1190.1 1190.2 1190.4 1190.5 1190.7 1190.8 1190.9 1191.1 1191.2 1191.3 1191.5 1191.6 1191.7 1191.9 1192.0 1192.1 1192.2 1192.4 1192.5 1192.6 1192.7 1192.9 1193.0 1193.1 1193.2 1193.3 1193.4 1193.5 1193.6 1193.8 1193.9 1194.0 1194.1 1194.3 1194.5 .1194.7 1194.9 1195.1 1195.3 1195.5 1195.7 . 1195.8 11%.0 11%.2 1196.4 1196.5 11%.7 11%. 9 1197.0 1197.2 1197.3 1197.5 1197.6 1197.8 1197.9 1198.1 1198.2 1198.4 1198.7 1199.0 1199.3 1199.6 1199.9 1200.1 1200.4 1200.6 1200.9 Specific Volume V Cu. ft. per lb. 4.049 4.015 3.981 3.947 3.914 3.882 3.850 3.819 3.788 3.758 3.728 3.699 3.670 3.642 3.614 3.587 3.560 3.533 3.507 3.481 3.455 3.430 3.405 3.381 3.357 3.333 3.310 3.287 3.264 3.242 3.220 3.198 3.177 3.155 3.134 3.114 3.094 3.074 3.054 3.034 3.015 2.977 2.940 2.904 2.869 2.834 2.801 2.768 i736 2.705 2.675 2.645 2.616 2.587 2.559 2.532 2.505 2.479 2.454 2.429 2.404 2.380 2.356 2.333 2.310 2.288 2.234 2 .*183 2.134 2.087 2.0422 1.9992 1.9579 1.9183 1.8803 CRANE APPENDIX A -- PHYSICAL PROPERTIES OP HU IDS AND PLOW CHARACTERISTICS OP VALVES, FITTINGS, ANDPIPE A- 15 Properties of Saturated Steam -- concluded Pressure Lbs. Per Sq. In. Temperature Heat of the Liquid Latent Heat of Evaporation Total Heat of Steam Absolute P' 250.0 255.0 260.0 265.0 270.0 275.0 280.0 285.0 290.0 295.0 300.0 320.0 340.0 360.0 380.0 400.0 420.0 440.0 460.0 480.0 500.0 520.0 540.0 560.0 580.0 600.0 620.0 640.0 660.0 680.0 700.0 720.0 740.0 760.0 780.0 800.0 820.0 840.0 860.0 880.0 900.0 920.0 940.0 960.0 980.0 1000.0 1050.0 1100.0 1150.0 1200.0 1250.0 1300.0 . 1350.0 1400.0 1450.0 1500.0 1600.0 1700.0 1800.0 1900.0 2000.0 2100.0 2200.0 2300.0 2400.0 2500.0 2600.0 2700.0 2800.0 2900.0 3000.0 3100.0 3200.0 3206.2 ! Gage !P 235.3 240.3 245.3 , 250.3 2.4.5.3 260.3 265.3 i 270.3 i 275.3 i 280.3 1 285.3 305.3 325.3 1 345.3 1 365.3 385.3 405.3 425.3 445.3 465.3 485.3 505.3 525.3 545.3 565.3 585.3 605.3 625.3 645.3 665.3' 685.3 705.3 725.3 745.3 765.3 785.3 805.3 825.3 845.3 865.3 885.3 905.3 925.3 945.3 965.3 985.3 1035.3 1085.3 1135.3 1185.3 1235.3 1285.3 1335.3 1385.3 1435.3 1485.3 1585.3 1685.3 1785.3 1885.3 1985.3 2085.3 2185.3 2285.3 2385.3 2485.3 2585.3 2685.3 2785.3 2885.3 2985.3 3085.3 3185.3 3191.5 t Degrees F. ! 400.vs i 402.70 404.42 406.11 ! 407.78 409.43 411.05 412.65 414.23 415.79 417.33 423.29 428.97 434.40 439.60 444.59 449.39 454.02 458.50 462.82 467.01 471.07 475.01 478.85 482.58 486.21 489.75 493.21 496.58 499.88 503.10 506.25 509.34 512.36 515.33 518.23 521.08 523.88 526.63 529.33 531.98 534.59 537.16 539.68 542.17 544.61 550.57 556.31 561.86 567.22 572.42 577.46 582.35 587.10 591.73 596.23 604.90 613.15 . 621.03 628.58 635.82 642.77 649.46 655.91 662.12 668.13 673.94 679.55 684.99 690.26 695.36 700.31 705.11 705.40 Btu/lb. 376.00 377.89 379.76 381.60 383.42 385.21 386.98 388.73 390.46 392.16 393.84 400.39 406.66 412.67 418.45 424.0 429.4 434.6 439.7 444.6 449.4 454.1 458.6 463.0 467.4 471.6 475.7 479.8 483.8 487.7 491.5 495.3 499.0 502.6 506.2 509.7 513.2 516.6 520.0 523.3 526.6 529.8 533.0 536.2 539.3 542.4 550.0 557.4 564.6 571.7 578.6 585.4 592.1 598.7 605.2 611.6 624.1 636.3 648.3 660.1 671.7 683.3 694.8 706.5 718.4 730.6 743.0 756.2 770.1 785.4 802.5 825.0 872.4 902.7 Btu/lb. 825.1 823.4 821.8 820.1 818.5 816.9 815.3 813.7 812.1 810.5 809.0 803.0 797.1 791.4 785.8 780.5 775.2 770.0 764.9 759.9 755.0 750.1 745.4 740.8 736.1 731.6 727.2 722.7 718.3 714.0 709.7 705.4 701.2 697.1 692.9 688.9 684.8 680.8 676.8 672.8 668.8 664.9 661.0 657.1 653.3 649.4 639.9 630.4 621.0 611.7 602.4 593.2 584.0 574.7 565.5 556.3 538.0 519.6 501.1 482.4 463.4 444.1 424.4 403.9 382.7 360.5 337.2 312.1 284.7 253.6 217.8 168.1 62.0 0.0 K Btu/lb. 1201.1 1201.3 1201.5 1201.7 1201.9 1202.1 1202.3 1202.4 1202.6 1202.7 1202.8 1203.4 1203.7 1204.1 1204.3 12Q4V5_, U204.O 1204^ 1204.6 1204.5 1204.4 1204.2 1204.0 1203.8 1203.5 1203.2 1202.9 1202.5 1202.1 1201.7 1201.2 1200.7 1200.2 1199.7 1199.1 1198.6 1198.0 1197.4 1196.8 1196.1 1195.4 1194.7 1194.0 1193.3 1192.6 1191.8 1189.9 1187.8 1185.6 1183.4 1181.0 1178.6 1176.1 1173.4 1170.7 1167.9 1162.1 1155.9 1149.4 1142.4 1135.1 1127.4 1119.2 1110.4 1101.1 1091.1 1080.2 1068.3 1054.8 1039.0 1020.3 993.1 934.4 902.7 Specific Volume V Cu. ft. per lb. 1.8438 1.8086 1.7748 1.7422 1.7107 1.6804 1.6511 1.6228 1.5954 1.5689 1.5433 1.4485 1.3645 1.2895 1.2222 1.1613 1.1061 1.0556 1.0094 0.9670 0.9278 0.8915 0.8578 0.8265 0.7973 . 0.7698 0.7440 0.7198 0.6971 0.6757 0.6554 0.6362 0.6180 0.6007 0.5843 0.5687 0.5538 0.5396 0.5260 0.5130 . 0.5006 0.4886 0.4772 0.4663 0.4557 0.4456 0.4218 0.4001 0.3802 0.3619 0.3450 0.3293 0.3148 0.3012 0.2884 0.2765 0.2548 0.2354 0.2179 0.2021 0.1878 0.1746 0.1625 0.1513 0.1407 0.1307 0.1213 0.1123 0.1035 0.0947 0.0858 0.0753 0.0580 0.0503 ,v \ A-16 appendix a-physical properties of fluids and flow characteristics of valves# fittings, and pipe CRANE g n n o n iBa m n iiiiio iif liiD B m Properties of Superheated Steam* V=specific volume, cubic feet per pound Ht=total heat of steam, Btu per pound Pressure Lbs. per Sq. In. Abs. Gage P' P Sat. Temp. t Total Temperature -- Degrees Fahrenheit (t) 360 400 440 480 500 600 700 800 900 1000 1200 14.696 0.0 212.00 V Hg 33.03 1221.1 34.68 1239.9 36.32 1258.8 37.96 1277.6 38.78 1287.1 42.86 1334.8 46.94 1383.2 51.00 1432.3 55.07 1482.3 59.13 1533.1 67.25 1637.5 20.0 5.3 227.96 V hg 24.21 1220.3 25.43 26.65 27.86 1239.2 1258.2 1277.1 28.46 1286.6 31.47 1334.4 34.47 37.46 1382.9 1432.1 40.45 1482.1 43.44 1533.0 49.41 1637.4 30.0 15.3 250.33 V hg 16.072 1218.6 16.897 17.714 18.528 18.933 1237.9 1257.0 1276.2 1285.7 20.95 22.% 24.% 1333.8 1382.4 1431.7 26.95 1481.8 28.95 1532.7 32.93 1637.2 40.0 25.3 267.25 V hg 12.001 1216.9 12.628 1236.5 13.247 1255.9 13.862 14.168 1275.2 1284.8 15.688 17.198 18.702 1333.1 1381.9 1431.3 20.20 1481.4 21.70 24.69 1532.4 1637.0 50.0 35.3 281.01 V h, 9.557 1215.2 10.065 1235.1 10.567 1254.7 11.062 11.309 1274.2 1283.9 12.532 13.744 14.950 1332.5 1381.4 1430.9 16.152 1481.1 17.352 1532.1 19.747 1636.8 60.0 45.3 292.71 V hg 7.927 8.357 8.779 9.196 9.403 10.427 11.441 12.449 13.452 14.454 16.451 1213.4 1233.6 1253.5 1273.2 1283.0 1331.8 1380.9 1430.5 1480.8 1531.9 1636.6 70.0 55.3. 302.92 V hg 6.762 7.136 7.502 7.863 1211.5 1232.1 1252.3 1272.2 8.041 1282.0 8.924 9.796 10.662 1331.1 1380.4 1430.1 11.524 1480.5 12.383 1531.6 14.097 1636.3 80.0 65.3 312.03 V hg 5.888 6.220 6.544 6.862 1209.7 1230.7 1251.1 1271.1 7.020 1281.1 7.797 8^562 9.322 1330.5 1379.9 1429.7 10.077 1480.1 10.830 1531.3 12.332 1636.2 90.0 75.3 320.27 V hg 5.208 1207.7 5.508 1229.1 5.799 1249.8 6.084 1270.1 6.225 1280.1 6.920 1329.8 7.603 1379.4 8.279 1429.3 8.952 1479.8 9.623 1531.0 10.959 1635.9 100.0 85.3 327.81 V hg 4.663 4.937 5.202 " 5.462 5.589 6.218 6.835 7.446 8.052 8.656 9.860 1205.7 1227.6 1248.6 1269.0 1279.1 1329.1 1378.9 1428.9 1479.5 1530.8 1635.7 120.0 105.3 341.25 V hg 3.844 4.081 1201.6 1224.4 4.307 1246.0 4.527 1266.9 4.636 1277.2 5.165 1327.7 5.683 1377.8 6.195 1428.1 6.702 1478.8 7.207 1530.2 8.212 1635.3 140.0 160.0 125.3 353.02 V hg 3.258 3.468 1197.3 1221.1 3.667 3.860 1243.3 1264.7 3.954 1275.2 4.413 4.861 1326.4 1376.8 5.301 1427.3 5.738 1478.2 6.172 1529.7 7.035 1634.9 145.3 363.53 V hg 3.008 3.187 3.359 3.443 3.849 4.244 4.631 5.015 5.3% 6.152 1217.6 1240.6 1262.4 1273.1 1325.0 1375.7 1426.4 1477.5 1529.1 1634.5 180.0 165.3 373.06 V hg 2.649 2.813 2.969 3.044 3.411 3.764 4.110 4.452 4.792 5.466 1214.0 1237.8 1260.2 1271.0 1323.5 1374.7 1425.6 1476.8 1528.6 1634.1 200.0 185.3 381.79 V h. 2.361 1210.3 2.513 1234.9 2.656 1257.8 2.726 1268.9 3.060 1322.1 3.380 1373.6 3.693 1424.8 4.002 1476.2 4.309 1528.0 4.917 1633.7 220.0 205.3 389.86 V hg 2.125 1206.5 2.267 1231.9 2.400 1255.4 2.465 1266.7 2.772 1320.7 3.066 1372.6 3.352 1424.0 3.634 1475.5 3.913 1527.5 4.467 1633.3 240.0 225.3 197.37 V hg ... 1.9276 2.062 2.187 2.247 2.533 2.804 3.068 3.327 3.584 4.093 1202.5 1228.8 1253.0 1264.5 1319.2 1371.5 1423.2 1474.8 1526.9 1632.9 260.0 280.0 300.0 320.0 245.3 404.42 V hg 265.3 411.05 V hg 285.3 417.33 V hg 305.3 423.29 V h,, 1.8882 1225.7 2.006 1250.5 2.063 1262.3 2.330 1317.7 2.582 1370.4 2.827 1422.3 3.067 1474.2 3.305 1526.3 3.776 1632.5 1.7388 1222.4 1.8512 1247.9 1.9047 1260.0 2.156 1316.2 2.392 1369.4 2.621 1421.5 2.845 1473.5 3.066 1525.8 3.504 1632.1 ... 1.6090 1219.1 1.7165 1245.3 1.7675 1257.6 2.005 1314.7 2.227 1368.3 2.442 1420.6 2.652 1472.8 2.859 1525.2 3,269 1631.7 1.4950 1215.6 1.5985 1242.6 1.6472 1255.2 1.8734 1313.2 2.083 1367.2 2.285 1419.8 2.483 1472.1 2.678 1524.7 3.063 1631.3 340.0 325.3 428.97 V hg 1.3941 1212.1 1.4941 1239.9 1.5410 1252.8 1.7569 1311.6 1.9562 1366.1 2.147 1419.0 2.334 1471.5 2.518 1524.1 2.881 1630.9 360.0 345.3 434.40 V hg ... 1.3041 1208.4 1.4012 1237.1 1.4464 1250.3 1.6533 1310.1 1.8431 1365.0 2.025 1418.1 2.202 1470.8 2.376 1523.5 2.719 1630.5 * Abstracted from Thermodynamic Properties of Steam by J. H. Keenan and F.G. Keyes, 1936 Edition, by permission of the publishers, John Wiley & Sons. Inc i (continued on the next page) CRANE APPENDIX A-PHYSICAL PROPERTIED OP FLUIDS AND flOW CHAHACTEMSTICS OP VALVES, FITTINGS, AND PIPE A-IT Properties of Superheated Steam -- continued V=specific volume, cubic feet per pound k,, = total heat of steam, Btu per pound IB S B B Q B B B S ilB S II BS Q&I & Pressure Lbs. per Sq. In. Abs. Gage P' P Sat. Temp. c Total Temperature -- Degrees Fahrenheit (t) 500 540 600 640 660 700 740 800 900 1000 1200 380.0 365.3 439.60 V hg 1.3616 1247.7 1.4444 1273.1 1.5605 1308.5 1.6345 1331.0 1.6707 1342.0 1.7419 1363.8 1.8118 1385.3 1.9149 1417.3 2.083 1470.1 2.249 1523.0 2.575 1630.0 400.0 385.3 444.59 V hg 1.2851 1245.1 1.3652 1271.0 1.4770 1306.9 1.5480 1329.6 1.5827 1340.8 1.6508 1362.7 1.7177 1384.3 1.8161 1416.4 1.9767 1469.4 2.134 1522.4 2.445 1629.6 420.0 405.3 449.39 V h, 1.2158 1242.5 1.2935 1268.9 1.4014 1305.3 1.4697 1328.3 1.5030 1339.5 1.5684 1361.6 1.6324 1383.3 1.7267 1415.5 1.8802 1468.7 2.031 1521.9 2.327 1629.2 440.0 425.3 454.02 V hg 1.1526 1239.8 1.2282 1266.7 1.3327 1303.6 1.3984 1326.9 1.4306 1338.2 1.4934 1360.4 1.5549 1382.3 1.6454 1414.7 1.7925 1468.1 1.9368 1521.3 2.220 1628.8 460.0 445.3 458.50 V hg 1.0948 1237.0 1.1685 1264.5 1.2698 1302.0 1.3334 1325.4 1.3644 1336.9 1.4250 1359.3 1.4842 1381.3 1.5711 1413.8 1.7124 1467.4 1.8508 1520.7 2.122 1628.4 480.0 465.3 462.82 V hg 1.0417 1234.2 1.1138 1262.3 1.2122 1300.3 1.2737 1.3038 1.3622 1.4193 1324.0 1335.6 1358.2 1380.3 1.5031 1.6390 1.7720 1412.9 1466.7 1520.2 2.033 1628.0 500.0 485.3 467.01 V 0.9927 h, 1231.3 1.0633 1.1591 1.2188 1.2478 1.3044 1260.0 1298.6. .1322.6 1334.2 1357.0 1.3596 1.4405 1.5715 1.69% 1379.3 1412.1 1466.0 1519.6 1.9504 1627.6 520.6 505.3 471.07 V hg 0.9473 1.0166 1228.3 1257.7 1.1101 12%. 9 1.1681 1321.1 1.1962 1332.9 1.2511 1355.8 1.3045 1378.2 1.3826 1.5091 1.6326 1411.2 1465.3 1519.0 1.8743 1627.2 540.0 525.3 475.01 V 0.9052 0.9733 1.0646 1.1211 1.1485 1.2017 1.2535 1.3291 1.4514 1.5707 1.8039 h, 1225.3 1255.4 1295.2 1319.7 1331.5 1354.6 1377.2 1410.3 1464.6 1518.5 1626.8 560.0 545.3 478,85 V hg 0.8659 0.9330 1222.2 1253.0 1.0224 1293.4 1.0775 1318.2 1.1041 1330.2 1.1558 1353.5 1.2060 1376.1 1.2794 1409.4 1.3978 1463.9 1.5132 1517.9 1.7385 1626.4 580.0 565.3 482.58 V hg 0.8291 0.8954 0.9830 1219.0 1250.5 1291.7 1.0368 1316.7 1.0627 1328.8 1.1131 1352.3 1.1619 1375.1 1.2331 1408.6 1.3479 1463.2 1.45% 1517.3 1.6776 1626.0 600.0 585.3 486.21 V 0.7947 0.8602 0.9463 0.9988 1.0241 1.0732 1.1207 1.1899 1.3013 1.40% 1.6208 hg 1215.7 1248.1 1289.9 1315.2 1327.4 1351.1 1374.0 1407.7 1462.5 1516.7 1625.5 620.0 605.3 489.75 V hg 0.7624 0.8272 0.9118 0.%33 0.9880 1.0358 1212.4 1245.5 1288.1 1313.7 1326.0 1349.9 1.0821 1373.0 1.1494 1406.8 1.2577 1461.8 1.3628 1516.2 1.5676 1625.1 640.0 625.3 493.21 V 0.7319 0.7962 0.8795 0.9299 0.9541 1.0008 1.0459 1.1115 1.2168 1.3190 `1.5178 hg 1209.0 1243.0 1286.2 1312.2 1324.6 1348.6 1371.9 1405.9 1461.1 1515.6 .1624.7 660.0 645.3 4%. 58 V hg 0.7032 1205.4 0.7670 1240.4 0.8491 1284.4 0.8985 1310.6 0.9222 1323.2 0.%79 1347.4 1.0119 1370.8 1.0759 1405.0 1.1784 1460.4 1.2778 1515.0 1.4709 1624.3 680.0 665.3 499.88 V hg 0.6759 0.7395 0.8205 1201.8 1237.7 1282.5 0.8690 0.8922 1309.1 1321.7 0.9369 0.9800 1346.2 1369.8 1.0424 1404.1 1.1423 1459.7 1.2390 1514.5 1.4269 1623.9 700.0 685.3 503.10 V hg 0.7134 0.7934 0.8411 0.8639 0.9077 0.9498 1.0108 1.1082 1.2024 1.3853 1235.0 1280.6 1307.5 1320.3 1345.0 1368.7 1403.2 1459.0 1513.9 1623.5 750.0 735.3 510.86 V hg 0.6540 0.7319 0.7778 0.79% 0.8414 0.8813 0.9391 1.0310. 1.11% 1.2912 1227.9 1275.7 1303.5 1316.6 1341.8 1366.0 1400.9 1457.2 1512.4 1622.4 800.0 785.3 518.23 V h. 0.6015 0.6779 0.7223 0.7433 0.7833 0.8215 0.8763 0.9633 1.0470 1.2088 1220.5 1270.7 1299.4 1312.9 1338.6 1363.2 1398.6 1455.4 1511.0 1621.4 850.0 835.3 525.26 V hg 0.5546 0.6301 0.6732 0.6934 0.7320 0.7685 0.8209 0.9037 0.9830 1.1360 1212.7 1265.5 1295.2 1309.0 1335.4 1360.4 13%.3 1453.6 1509.5 1620.4 900.0 885.3 531.98 V hg 0.5124 0.5873 0.6294 0.6491 0.6863 0.7215 0.7716 0.8506 0.9262 1.0714 1204.4 1260.1 1290.9 1305.1 1332.1 1357.5 1393.9 1451.8 1508.1 1619.3 950.0 935.3 538.42 V hg 0.4740 0.5489 0.5901 0.6092 0.6453 0.6793 0.7275 0.8031 0.8753 1.0136 1195.5 1254.6 1286.4 1301.1 1328.7 1354.7 1391.6 1450.0 1506.6 1618.3 1000.0 985.3 544.61 V hg 0.5140 0.5546 0.5733 0.6084 0.6413 0.6878 0.7604 0.8294 0.%15 1248.8 1281.9 1297.0 1325.3 1351.7 1389.2 1448.2 1505.1 1617.3 -%t4** A-18 APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Properties of Superheated Steam -- concluded V=specific volume, cubic feet per pound hs = total heat of steam, Btu per pound Pressure Lbs. Sq. r Abs. Gage P' P Sat. Temp. t Total Temperature -- Degrees Fahrenheit (t) 660 700 740 760 780 800 860 900 1000 1100 1200 1100.0 1085.3 556.31 V1 kg 0.5110 1288.5 0.5445 0.5755 0.5904 0.6049 0.6191 0.6601 0.6866 0.7503 1318.3 1345.8 1358.9 1371.7 1384.3 1420.8 1444.5 1502.2 0.8117 0.8716 1558.8 1615.2 1200.0 1185.3 567.22 V hg 0.4586 1279.6 0.4909 0.5206 0.5347 1311.0 1339.6 1353.2 0.5484 0.5617 0.6003 1366.4 1379.3 1416.7 0.6250 0.6843 1440.7 1499.2 0.7412 1556.4 0.7%7 1613.1 1300JO 1285.3 577.46 V hg 0.4139 1270.2 0.4454 0.4739 1303.4 1333.3 0.4874 1347.3 0.5004 1361.0 0.5131 1374.3 0.54% 1412.5 0.5728 1437.0 0.6284 0.6816 1496.2 1553.9 0.7333 1611.0 1400.0 1385.3 587.10 V hg 0.3753 1260.3 0.4062 1295.5 0.4338 1326.7 0.4468 1341.3 0.4593 1355.4 0.4714 1369.1 0.5061 1408.2 0.5281 1433.1 0.5805 1493.2 0.6305 1551.4 0.6789 1608.9 1500.0 1485.3 596.23 V hg 0.3413 1249.8 0.3719 1287.2 0.3989 1320.0 0.4114 1335.2 0.4235 1349.7 0.4352 1363.8 0.4684 1403.9 0.4893 1429.3 0.5390 0.5862 1490.1 1548.9 0.6318 1606.8 1600.0 1585.3 604.90 V hg 0.3112 1238.7 0.3417 1278.7 0.3682 0.3804 1313.0 1328.8 0.3921 1343.9 0.4034 1358.4 0.4353 1399.5 0.4553 1425.3 0.5027 1487.0 0.5474 1546.4 0.5906 1604.6 1700.0 1685.3 613.15 V hg 0.2842 1226.8 0.3148 1269.7 0.3410 1305.8 0.3529 1322.3 0.3643 1337.9 0.3753 1352.9 0.4061 1395.0 0.4253 1421.4 0.4706 1484.0 0.5132 1543.8 0.5542 1602.5 1800.0 1785.3 621.03 V kg 0.2597 0.2907 1214.0 1260.3 0.3166 1298.4 0.3284 1315.5 0.3395 1331.8 0.3502 1347.2 0.3801 1390.4 0.3986 0.4421 1417.4 1480.8 0.4828 1541.3 0.5218 1600.4 1900.0 1885.3 628.58 V hg 0.2371 0.2688 0.2947 0.3063 0:3173 0.3277 0.3568 0.3747 1200.2 1250.4 1290.6 1308.6 1325.4 1341.5 1385.8 1413.3 0.4165 0.4556 0.4929 1477.7 1538.8 1598.2 2000.0 1985.3 635.82 V hg 0.2161 0.2489 0.2748 0.2863 0.2972 0.3074 1184.9 1240.0 1282.6 1301.4 1319.0 1335.5 0.3358 1381.2 0.3532 0.3935 0.4311 0.4668 1409.2 1474.5 1536.2 15%. 1 2100.0 2085.3 642.77 V hg 0.1962 0.2306 0.2567 0.2682 0.2789 0.2890 0.3167 0.3337 0.3727 0.4089 0.4433 1167.7 1229.0 1274.3 1294.0 1312.3 1329.5 1376.4 1405.0 1471.4 1533.6 1593.9 2200.0 2185.3 649.46 V h{ 0.1768 1147.8 0.2135 1217.4 0.2400 0.2514 1265.7 1286.3 0.2621 0.2721 0.2994 0.3159 1305.4 1323.3 1371.5 1400.8 0.3538 1468.2 0.3887 1531.1 0.4218 1591.8 2300.0 2285.3 655.91 V 0.1575 0.1978 0.2247 0.2362 0.2468 0.2567 0.2835 0.2997 0.3365 0.3703 0.4023 hg 1123.8 1204.9 1256.7 1278.4 1298.4 1316.9 1366.6 13%.5 1464.9 1528.5 1589.6 2400.0 2385.3 662.12 V hg 0.1828 0.2105 0.2221 0.2327 0.2425 0.2689 0.2848 0.3207 0.3534 0.3843 1191.5 1247.3 1270.2 1291.1 1310.3 1361.6 1392.2 1461.7 1525.9 1587.4 2500.0 2485.3 668.13 V hg 0.1686 0.1973 0.2090 0.2196 0.2294 0.2555 0.2710 0.3061 0.3379 0.3678 1176.8 1237.6 1261.8 1283.6 1303.6 1356.5 1387.8 1458.4 1523.2 1585.3 2600.0 2585.3 673.94 V hg 0.1549 0.1849 0.1967 0.2074 0.2172 0.2431 0.2584 0.2926 0.3236 0.3526 1160.6 1227.3 1252.9 1275.8 12%. 8 1351.4 1383.4 1455.1 1520.6 1583.1 2700.0 2685.3 679.55 V hg 0.1415 0.1732 0.1853 0.1960 0.2059 0.2315 0.2466 0.2801 0.3103 0.3385 1142.5 1216.5 1243.8 1267.9 1289.7 1346.1 1378.9 1451.8 1518.0 1580.9 2800.0 2785.3 684.99 V hg 0.1281 0.1622 0.1745 0.1854 0.1953 0.2208 0.2356 0.2685 0.2979 0.3254 1121.4 1205.1 1234.2 1259.6 1282.4 1340.8 1374.3 1448.5 1515.4 1578.7 2900.0 2885.3 690.26 V hg 0.1143 0.1517 0.1644 0.1754 0.1853 0.2108 0.2254 0.2577 0.2864 0.3132 1095.9 1193.0 1224.3 1251.1 1274.9 1335.3 1369.7 1445.1 1512.7 1576.5 3000.0 2985.3 695.36 V hg 0.0984 0.1416 0.1548 0.1660 0.1760 0.2014 0.2159 0.2476 0.2757 0.3018 1060.7 1180.1 1213.8 1242.2 1267.2 1329.7 1365.0 1441.8 1510.0 1574.3 3100.0 3085.3 700.31 V hg 0.1320 0.1456 0.1571 0.1672 0.1926 0.2070 0.2382 0.2657 0.2911 1166.2 1202.9 1233.0 1259.3 1324.1 1360.3 1438.4 1507.4 1572.1 3200.0 3185.3 705.11 V hg 0.1226 0.1369 0.1486 0.1589 0.1843 0.1986 0.2293 0.2563 0.2811 1151.1 1191.4 1223.5 1251.1 1318.3 1355.5 1434.9 1504.7 1569.9 3206.2 3191.5 705.40 V hg 0.1220 0.1363 0.1480 0.1583 0.1838 0.1981 0.2288 0.2557 0.2806 1150.2 1190.6 1222.9 1250.5 1317.9 1355.2 1434.7 1504.5 1569.8 IB B B B B B B B B B B flt H f8 g g B8 8 t 1 1 H .H CRANE APPENDIX A -- PHYSICAL PHOPEKTIES OF FLUIDS AND HOW CHAPACTEPISTICI OF VALVES, FITTINGS, AND PIPE Flow Coefficient C for Nozzles7 Data from Regelnfuer die Durch- flussmessung mil genormten D[uesen und Bienden. VDl-Verlag G. m.b. H.. Berlin. 5NW, 7, 1937. Published as Technical Memo randum 952 by the NACA. A-19 Ratio of Nozzle Diameter to Pipe Diameter Example: The flow coeffi cient C for a diameter ratio do/di of o.6o at a Reynolds number of 20,000 (2 x 104) equals 1.01. Flow Coefficient C for Square Edged Orifices7,17 c Ratio of Orifice Diameter to Pipe Diameter W f aa a a a a (i^ di ^ Inside </0 Dia. of--[-- Pipe Flow ........... A-20 tsosMMta; APPENDIX A --PHYSICAL PROPERTIES OF FLUIDS AND FlOW CHARACTERISTICS OP VALVES. FITTINGS, AND PIPE CRANE Net Expansion Factor, Y For Compressible Flow through Nozzles and Orifices9,10 antD Bnunman 8m m m mona k = 1.45 1............................ .. I i . i I i i i i I i i_. i 1 i i i i I i i i i i ,, i , I , i i 11 0 .2 .4 , .6 .8 1.0 k = 1.40 I i i i i I i i i i I i i i i I i i i I i i i i 1 L i i i 1 i i i i I i i i i l i i i i I i i i i I 0 .2 .4 , .6 , , .8 1.0 k = 1.35 I t i i i t i i i i i i i i i i I < i J-Li i t-Li-i t-i.-t i i i l i i i i i i i i > 0 .2 .4 .6 .8 1.0 k = 1.30 11 i i i i i I I t i i i I i < l < i i I l ' I 0 .2 .4 .6 .8 1.0 k = 1.25 Li i i i I i i i i I i i i i I i i i I i i i I i i i i 1 i i i i I i i i I i i i i I t i i i I 0 .2 .4 .6 .8 1.0 Pressure Ratio -- A P Pi Di^aatuaj ecAxtirioacbtiecud furuomui Fi'tlutiud Mjvteetieerrss;, Ti hnetiirr T1 hneeovrryy acunmd Application,. Fourth Edition,. 1937,. and Orifice Meiers with' S~upercritical.F.low.by R. G. Cunningham, with permission of the publisher, The American Society of Mechanical Engineers, 29 WWeest 3- -9th S- treet, N` 'ew 'Y'or'k '1"8. CRANE APPENDIX A-PHYSICAL PtOPStTltS OF PIUIDS AND FtOVACHAHACTCTISTICS OP VAIVES. FITTINGS, AND PIPE Critical Pressure Ratio, re For Compressible Flow through Nozzles and Venturi Tubes9 a-at ** t t hgeb \f A-22 APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE Net Expansion Factor Y for Compressible Flow Through Pipe to a Larger Flow Area CRANE k = 1.3 Limiting Factors For Sonic Velocity k = 1.3 K AP P'i y 1.2 1.5 2.0 3 4 6 8 10 15 20 40 100 .525 .612 .550 .631 .593 .635 .642 .658 .678 .670 .722 .685 .750 .698 .773 .705 .807 .718 .831 .718 .877 .718 .920 .718 k = 1.4 AP P[ Limiting Factors For Sonic Velocity k = 1.4 K AP P'i y 1.2 1.5 2.0 3 4 6 8 10 15 20 40 100 .552 .588 .576 .606 .612 .622 .662 .639 .697 .649 .737 .671 .762 .685 .784 .695 .818 .702 .839 .710 .883 .710 .926 .710 <8 E* CRANE APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOWXHAHACTtmSTICS OF VALVES, FITTINGS, AND PIPE Relative Roughness of Pipe Materials and Friction Factors For Complete Turbulence18 Pipe Diameter, in Feet-D A-23 Data extracted from Friction Factors for Pipe Flow by L.F. Moody, with permission of the publisher, The American Soci ety of Mechanical Engineers, 29 West 39th Street, New York. Problem: Determine absolute and relative roughness, and friction fac tor, for fully turbulent flow in 10-inch cast iron pipe (I.D. = 10.16'). Solution: Absolute roughness (e) = 0.00085........ Relative roughness (e/D) = 0.001... Friction factor at fully turbulent flow (/) = o.oiq6. A-24APPENDIX A-PHYSICAL PROPERTIES OF FUNDS AND FLOW CHARACTERISTICS Of VAIVES, FITTINGS, AND PIPE Friction Factors for Any Type of Commercial Pipe18 0>3 Ca(/O>> -- a> asso az oos C RA U f >> c Jl ^oZ ->*1 S<u'o--o* |Wv x&Z *-^w H c-S -- <n 4J 2 Jj gi* t*. sS E ** c |o| sl't b >w< h&S- a4ca-d1 .-tC>_l .O 8o <o sO o sCoO 4O-4 xoetc5O 6- _uQ ^ co &tiD133 oQ* OV' y0) >""V. i- i > CO u rrCt*O> *zos* u oI2 og CJ XtiDwCO3 P .c2 C0-- q~co 'Z>j .2 JO 0uu) X^w uQ . 4J <y %s> Hc CD *.X p t fiH ies Q JSPDQoCl) ttateJ*g2* oo CRANE APPENDIX A-PHYSICAL'PROPERTIES Of FLUIDS AND FLOW CHARACTERISTICS Of VALVES, FITTINGS, AND FIFE Friction Factors for Clean Commercial Steel and Wrought Iron Pipe18 A-25 S olution: The frictio n factor ( / ) equals 0.016. P ro b le m : Determ ine the friction factor for 12-inch Schedule 40 pipe a t a flow having a Reynolds num ber o f 300,000, B gBBBBB iffU tB B B lll l i i i i i i m m ii-t- .1-slS 5 5 a s> - Ki 11 m too S to I Resistance Coefficient- WHHHH A -26APPENDIX A-PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Resistance in Pipe Resistance Due to Sudden Enlargements and Contractions20 djdz Sudden enlargement: The resist ance coefficient K for a sudden en largement from 6-inch Schedule 40 pipe to li-inch Schedule 40 pipe is 0.55, based on the 6-inch pipe size. A 6.065 0.51 di 11.938 Sudden contraction: The resist ance coefficient K for a sudden con traction from 12-inch Schedule 40 pipe to 6-inch Schedule 40 pipe is 0.33. based on the 6-inch pipe size. --dd\i = -6--.-0-6--5= n.938 0.51 Note: The values for the resistance coefficient, K, are based on velocity in the small pipe. To determine K values in terms of the greater diam eter, multiply the chart values by (dt/dO*. Resistance Due to Pipe Entrance and Exit K = 0.78 Inward Projecting Pipe Entrance K = 0.50 Sharp Edged Entrance K = 1.0 Projecting Pipe Exit K= 1.0 Sharp Edged Exit K = 0.23 Slightly Rounded Entrance K = 1.0 Rounded Exit K = 0.04 Well Rounded Entrance Problem: Determine the total re sistance coefficient for a pipe one diameter long having a sharp edged entrance and a sharp edged exit. Solution: The resistance of pipe one diameter long is small and can be neglected (K -- f L/D). From the diagrams, note: Resistance for a sharp edged entrance = 0.5 Resistance for a sharp edged exit = 1.0 Then, the total resistance, K, for the pipe = 1.5 CRANE APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND FIFE Resistance of Bends Resistance of 90 Degree Bends21 The chart at the right shows the resistance of qo degree bends to the flow of fluids in terms of equivalent lengths of straight pipe. Resistance of bends greater than qo degrees is found using the formula: ,, -r,+o-o(r,+&) n = total number of *50 bends in coil R, = total resistance due to one 90 bend, in L/D R i = resistance due to length of one 90 bend, in L/D Rs = bend resistance due to one 90 bend, in L/D Problem: Determine the equivalent lengths in pipe diameters of a qo degree bend and a 270 degree bend having a relative radius of 12, Solution: Referring to the "Total Resist ance" curve, the equivalent length for a 90 degree bend is 34.5 pipe diameters. The equivalent length of a 270 degree bend is: L/D = 34.5 + (3 - 0 [18.7 + (15.8 2)] L/D = 87.7 pipe diameters Note: This loss is less than the sum of losses through three qo degree bends separated by tangents. For "resistance of bends theory", see page 2-i2. ' Chart for Rosistanco of 90 Oosroo Bonds From Pressure Losses for Fluid Flow in 90 Degree Pipe Bends by K. H. Beij. Courtesy of Journal of Research of National Bureau of Standards, Vol. 21, July, 1938. A-27 Resistance of Miter Bends4 The chart at the lower right shows the re sistance of miter bends to the flow of fluids. The chart is based on data published by the American Society of Mechanical Engineers (ASME). . Problem: Determine the equivalent length in pipe diameters of a 40 degree miter bend. Solution: Referring to the "Total Resist ance" curve in the chart, the equivalent length is 12 pipe diameters. Chart far Rosistanco of Mltor Bonds giB B B B B D iinnH B B B flflonnangflfla a ig e A - 28 APPENDIX A -- PHYSICAL PROPERTIES OP FLUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE Types of Valves CRANE V Conventional Globe Valve Conventional Globe Valve With Disc Guide ' Conventional Angle Valve Y-Pattern Globe Valve With Stem 60 degrees from Run Conventional Swing Check Valve Clearway Swing Check Valve Globe Type Lift Check Valve a ana n o o o o o n e Angle Slop-Check Valve Poppet Type Hinged Typo i In-line Ball Check Valve Three-Way Cock Sectional and Outside Views ajjafijUfajaMriln nn-- A-30 APPENDIX A -- PHYSICAl PROPERTIES Of FLUIDS AND HOW CHARACTERISTICS OF VALVES, HTTINOS, AND PIPE CRANE Schedule (Thickness) of Steel Pipe Used in Obtaining Resistance Of Valves and Fittings of Various Pressure Classes by Test* Valve or Fitting ASA Pressure Classification (Steam Rating) 250-Pound and Lower 300-Pound to 600-Pound 900-Pound 1500-Pound . 2500-Pound Sizes Vv to 6-inch Sizes 8-inch and larger Schedule No. of Pipe (Thickness) Schedule 40 Schedule 80 Schedule 120 Schedule 160 xx (Double Extra Strong) Schedule 160 ""These schedule numbers have been arbi trarily selected only for the purpose of identifying the various pressure classes of valves and fittings with specific pipe dimensions for the interpretation of flow test data; they should not be construed as a recommendation for installation purposes. Representative Equivalent Length* in Pipe Diameters (L/D) Of Various Valves and Fittings Description of Product Equivalent Length In Pipe Diameters (L/D) Globe Valves Conventional Y-Pattem With no obstruction in flat, bevel, or plug type seat With wing or pin guided disc (No obstruction in flat, bevel, or plug type seat) - With stem 60 degrees from run of pipe line - With stem 45 degrees from run of pipe line Fully open Fully open Fully open Fully open 340 450 175 145 Angle Valves Conventional With no obstruction in flat, bevel, or plug type seat With wing or pin guided disc Fully open Fully open 145 200 Conventional Wedge Disc, Double Disc, or Plug Disc Gate Fully open Three-quarters open One-half open One-quarter open 13 35 160 900 Valves Pulp Stock Fully open Three-quarters open One-half open One-quarter open 17 50 260 1200 Conduit Pipe Line - Fully open 3* Check Valves Conventional Swing Clearway Swing Globe Lift or Stop Angle Lift or Stop In-Line Ball .... , 0.5 f. .Fully open 135 ' ~'^-^0.5f.. .Fully open 50 2.t)t- Fully open Same as Globe 2.0f... Fully open Same as Angle 2.5 vertical and 0.25 horizontalf.. .Fully open 150 Foot Valves with Strainer With poppet lift-type disc With leather-hinged disc 0.3f.. .Fully open 0.4f. . Fully open 420 75 Butterfly Valves (6-inch and larger) Fully open 20 Cocks Straight-Through Three-Way Rectangular plug port area equal to 100% of pipe area Fully open Rectangular plug port area equal to 80% of pipe area (fully open) Flow straight through Flow through branch 18 44 140 90 Degree Standard Elbow 45 Degree Standard Elbow 90 Degree Long Radius Elbow ` 30 16 20 90 Degree Street Elbow Fittings 45 Degree Street Elbow Square Comer Elbow 50 26 57 Standard Tee With flow through run With flow through branch 20 60 Close Pattern Return Bend 50 Pipe 90 Degree Pipe Bends Miter Bends Sudden Enlargements and Contractions Entrance and Exit Losses See Page A-27 See Page A-27 See Page A-26 See Page A-26 **Exact equivalent length is equal to the length between flange faces or welding ends. tMinimum calculated pressure drop (psi) across valve to provide sufficient flow to lift disc fully. JFor limitations, see page 2-11. For effect of end connections, see page 2-10. For raditanc* factor "K", quiro/wif length in fit 'of pip*, and equivahnt flow coeffidtnt "Cv", pagn A-3I and A-32. A-32 i i,hbI jnirtMiTt APPENDIX A-PHYSICAL PROPERTIES OP FLUIDS AND HOW CHARACTERISTICS OF VALVES, PITTINGS, AND PIPE CRANE '"Equivalents of Resistance Coefficient K And Flow Coefficient Cv // K r--0.1 jo.15 -0.2 I--0.3 E"0.4 -0.5 H0.6 PO.7 -0.8 S -0.9 S -1.0 0O3 O -L5 - c&+-5> -2- *QcSo I M --15 E-20 --24 r 897 d4 A------- pj--- 'v 29.9 d2 c' = yir Cv p-60,000 r50,ooo --40,000 - 30,000 E-20,000 --10,000 -8000 r6000 -5000 -4000 r--3000 -2000 Problem: Find the equivalent length in pipe diameters, the resistance coefficient K, and the flow coefficient CT for an 8-inch, 125-pound Y-pattem globe valve with stem 60 degrees from run of valve. Solution: Equivalent length in pipe diameters is 175 (taken from table shown on page A-30) Resistance factor K based on Schedule 40 pipe is 2.5 (taken from chart shown on preceding page) Flow coefficient CT is 1200 (see dotted line shown on chart above). *Fer limitation*, m page 2-M. rioo i ' =80 ^ -60 -50 1-40 r-30 =-20 = 10 --8 E-6 -5 -4 3 -2 L-l 1.0 1 .9-1 t--3/4 .7-- .6 --J--1/2 .5 -- 3/8 .4 --1 m Engineering Data i -------------i n ---- - ------- ~ ........ ..... ... . ................................ ...... ........ .................-- -- ...... - " - j ggami 118non mi ii eii m u Flow problems are encountered in many fields of engineering; therefore, a wide choice of terminology prevails. Terms most widely accepted in the fluid dynamics field have been employed in this paper. In the event problems are expressed in units other than used in this paper, tables and nomographs are provided for conversion. Other useful engineering data are presented to pro vide direct solutions to frequently recurring factors appearing in flow formulas, as well as complete solutions to water and air flow pressure drop problems. . B-2 APPENDIX B- ENGINEERING DATA Equivalent Volume and Weight Flow Rates of Compressible Fluids Q'd Rate of Flow, in Millions of Cubic Feet per Day at Standard Conditions- q'd 1000 800 " 600 400 qm 1000 -60,000 800-40,000 600--I-30,000 400 -20,000 300 300200-- 200J-10,000 _ 100- -6000 100- -4000 60--f-3000 | 60-- 40--r 1 -2000 S 40 ! 30- ca tZ 30- * 20 1 -1000^ 5 20-- * i--800~~ - 8. 8. 10- -600- "S 10 -400 " 6- 8 -300 6 I 4--I - e .-1i--200 4 3- I 2 - -s j-ioo s 2-- -80 -i .S i.o- -60 0.8- 1 1--40 0.8 0.6-| -30 or ` 0.6 0.4 -20 0.3 0.4 0.3 0.2- d--io 0.2- -8 0.1 -6 .080.1- -4 w r-10,000 -8000 -6000 -5000 -4000 -3000 -2000 -1000 j-800 -600 -500 -400 -300 -200 -100 ai/% -80 f =60 "50 '! -40 1 -3o0n ^o -20 "s -l.o -0.8 --0.6 --0.5 -0.4 --0.3 -0.2 --0.1 W = 4.58 q'm S,, W = Pa q\ S, W = 0.0764 q'n Se W = 3180 q'n S, where: . pa = weight density of air at standard conditions (14.7 psia and 60 F) Problem: What is the rate of flow in pounds per hour of a gas, which has a specific gravity of 0.78, and is flowing at the rate of 1.000.000 cubic feet per hour at standard conditions' Solution: W = 50.000 pounds per hour. CRANE Si 2.7- 2.5- 2.0- -- 1.5- C* w 1 1.0-- CoD -- cS/o. 0.9-- I *3a 0.7 | 0.5--J 0.4--| 0.35--1 m* w CRANE aekndix s-engineering data Equivalents of Absolute Viscosity B-3 Absolute or Dynamic Viscosity Centipoise Centipoise Poise Gram Cm Sec Dyne Sec Cm* 00 (100 m) GO 1 100 Poise Gram Cm Sec Dyne Sec Cm* (100 m) 0.01 1 Slugs Ft Sec `Poundr Sec Ft* " (m') 2.09 (10"5) 2.09 (10-*) fPound*, Ft Sec Poundal Sec Ft* (.) 6.72 (10-<) 0.0672 Slugs Ft Sec 'Pound/ Sec Ft* 0*'.) 47 900 479 1 g or 32.2 fPoundm Ft Sec Poundal Sec Ft* (l*e) 1487 *Pound/= Pound of Force 14.87 -- or .0311 g fPoun^m= Pound of Mass 1 To convert absolute or dynamic viscosity from one set of units to another, locate the given set of units in the left hand column and multiply the numerical value by the factor shown horizontally to the right under the set of units desired. As an example, suppose a given absolute viscosity of z poise is to be converted to slugs/foot second. By referring to the table, we find the conversion factor to be 2.09 (io-3). Then, z (poise) times z.og (io-3)' = 4.18 (10-3) = 0.00418 slugs/foot second. Equivalents of Kinematic Viscosity Kinematic Viscosity Centistokes Centistokes Stokes Cm* Sec Ft* Sec M (100 v) W) M 1 100 92 900 Stokes Cm* Sec (100 >0 0.01 1 929 Ft*. Sec M 1.076 (10-5) 1.076 (10-*) 1 To convert kinematic viscosity from one set of units to another, locate the given set of units in the left hand column and multiply the numerical value by the factor shown horizontally to the right, under the set of units desired. As an example, suppose a given kinematic viscosity of 0.5 square foot/second is to be converted to centistokes. By referring to the table, we find the con version factor to be 92,900. Then, 0.5 (sq ft/sec) times 92,900 = 46,450 centistokes. For conversion from kinematic to abso/ufe viscosity, see page B-5. B-4 n '-'rViaTigai>rt6<i~ ,*S~, ---**---- K APKeiwIX b-engineering data CRANE Equivalents of Kinematic and Saybolt Universal Viscosity Equivalents of Kinematic and Saybolt Furol Viscosity at 122 F Kinematic Equivalent Kinematic Equivalent Viscosity Saybolt Universal Viscosity Saybolt Universal Viscosity, Sec Viscosity, Sec Centistokes At 100 F At Centistokes At 100 F V Basic ' 210 F V Basic Values Values At 210 F 2.0 2.5 3.0 3.5 4.0 4.5 5 6 7 .. 8 9 10 11 12 13 14 15 16 17 18 19 32.6 34.4 36.0 37.6 39.1 40.8 42.4 45.6 48.8 52.1 55.5 58.9 62.4 66.0 69.8 73.6 77.4 81.3 85.3 89.4 93.6 32.9 34.7 36.3 37.9 39.4 41.0 42.7 45.9 49.1 52.5 55.9 59.3 62.9 66.5 70.3 74.1 77.9 81.9 85.9 90.1 94.2 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 136.9 141.3 145.7 150.2 154.7 159.2 163.7 168.2 172.7 177.3 181.8 186.3 190.8 195.3 199.8 204.4 209.1 213.7 218.3 222.9 227.5 137.9 142.3 146.8 151.2 155.8 160.3 164.9 169.4 173.9 178.5 183.0 187.6 192.1 196.7 201.2 205.9 210.5 215.2 219.8 224.5 229.1 20 97.8 98.5 50 232.1 233.8 21 102.0 102.8 55 255.2 257.0 22 106.4 107.1 60 278.3 280.2 23 110.7 111.4 65 301.4 303.5 24 115.0 115.8 70 324.4 326.7 25 119.3 120.1 Saybolt Seconds 26 123.7 124.5 Over 70 equal 27 128.1 129.0 Centistokes 28 132.5 133.4 x 4.635 x 4-667 Note: To obtain the Saybolt Universal viscosity, equiva lent to a kinematic viscosity determined at t, multiply the equivalent Saybolt Universal viscosity at 00 F by i + (t -- IOO) 0.000 064. For example, lo^atzioF are equivalent to 58.9 multi plied by 1.0070 or 59.3 sec Saybolt Universal at 210 F. Kinematic Viscosity Centistokes v Equiv Kinematic alent Viscosity Saybolt Furol Viscosity, Centistokes Sec V Equiv alent Saybolt Viscosity, Sec 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 -- 94 96--. 98 100 105 110 115 120 125 130 135 140 145 25.3 26.1 27.0 27.9 28.8 29.7 30.6 31.5 32.4 33.3 34.2 35.1 36.0 36.9 37.8 38.7 39.6 40.5 41.4 42.3 43.2 44.1 45.0 45.9 46.8 47.7 48.6 50.9 53.2 55.5 57 *8 60.1 62.4 64.7 67.0 69.4 150 71.7 155 74.0 160 76.3 165 78.7 170 81.0 175 83.3 180 85.6 185 88.0 190 90.3 195 92.6 200 95.0 210 99.7 220 104.3 230 109.0 240 113.7 250 118.4 260 123.0 270 127.7 280 132.4 290 137.1 300 141.8 310 146.5 320 151.2 330 155.9 340 160.6 350 165.3 360 170.0 370 174.7 380 179.4 390 184.1 400 Over 400 Saybolt Furol Seconds = Centistokes x 0.4717 These tables are reprinted with the permission of the American Society for Testing Materials (ASTM). The table at the left was abstracted from D446-53, as shown on page 226 of ASTM Standards, Part 5, 1955 edition. The table at the right was abstracted from D 666-53, as shown on page 302 of ASTM Standards, Part 5, 1955 edition. UdHW W ? CRANE APPENDIX E-- ENGINEERING DATA Equivalents of Kinematic Saybolt Universal Saybolt Furol, and Absolute Viscosity B-5 1000 io.ooo 900 800 700 600 500 400 to 300 v 2000 1000 900 800 700 600 s 150-- -300 1100 90 80 70 60 1000 -f -200 .01 .009 .008 0 .007 <S .006 $ .005 V) M .004 -500 >Q0 1-300 ; i-200 50 40 3026 - 500H -100 1 | .003 -1 400- -90 3 g 8Q..S 2 .002 -%;--,91000 'C. -70 300- -60 -50 200- -c_<n %uin > 2 ."t>sL 53 .001 r70 ; -50 >oi ..0u0n0t0nii00nra98 .0007 --^a=-r4mU .2 5O 1 E-30 1 .0006 - 30 a. 43 100 _T S- _ 20 I09 90 ~ 80 .0005.0004 -20 .0003-i a 70-% 'to --y- y -- vS The empirical relation between Saybolt Universal Viscosity and Saybolt Furol Viscosity at ioo F and nz F, respectively, and Kinematic Viscosity is taken from A.S.T.M. D446-53 and D666-53. At other temperatures, the Saybolt Viscosities vary only slightly. Saybolt Viscosities above those shown are given by the rela tionships : Saybolt Universal Seconds = Centistokes x 4.635 Saybolt Furol Seconds = Centistokes x 0.470 s 1.3--1 1-2-1 Gravity, in Degrees API fc-3 35- C-2 .00003-if .00002%: .00001-3"1 Problem Is Determine the absolute viscosity of an oil which has a kinematic viscosity of 82 centistokes and a specific gravity of 0.83. Solution 1: Connect 82 on the kinematic vis cosity scale with 0.83 on the specific gravity scale; read 67 centipoise at the intersection on the absolute viscosity scale. Problem 2: Determine the absolute viscosity of an oil having a specific gravity of 0.83 and a Saybolt Furol viscosity of 40 seconds. Solution 2: Connect 0.83 on the specific gravity scale with 40 seconds on the Saybolt Furol scale; read 67 centipoise at the intersection on the absolute Mscosity scale. B-6 gg IS 3 aas c APPENDIX B- ENGINEERING DATA Saybolt Universal Viscosity Chart SQNCD3S 1VSH3AINI1 J.1O0AVS `A11S03SIA CRANE TEMPERATURE, DECREES FAHRENHEIT s 8oo31o 8o 8 o8 8 3n 8 8 3N 8-* g g 8 S S g S a s ""r " ~ ~ " SQN0D3S 1VSS3AINI1AIOBAVS \UISCOSJA CRANE APPENDIX B-ENGINEERING DATA Equivalents of Degrees API/ Degrees Baum&, Specific Gravity, Weight Density, and Pounds Per Gallon at 60F/60F B-7 g Bg B-KBBEBBBgBBganIHU H Degrees on API or Baume Scale Values for API Scale Oil Specific Gravity Weight Density, Lb/Ft3 Pounds per Gallon SP 0 2 4 6 8 10 1.0000. 12 0.9861 14 0.9725 16 0.9593 18 0.9465 20 0.9340 22 0.9279 24 0.9100 26 0.8984 28 0.8871 30 0.8762 32 0.8654 34 0.8550 36 0.8448 38 0.8348 40 0.8251 42 0.8155 44 0.8063 46 0.7972 48 0.7883 50 0.7796 52 0.7711 54 0.7628 56 0.7547 58 0.7467 60 , 0.7389 62 0.7313 64 0.7238 66 0.7165 68 0.7093 70 0.7022 72 0.6953 74 0.6886 76 0.6819 78 0.6754 80 0.6690 82 0.6628 84 0.6566 86 0.6506 88 0.6446 90 0.6388 92 0.6331 94 0.6275 % 0.6220 98 0.6166 100 0.6112 62.36 61.50 60.65 59.83 59.03 58.25 57.87 56.75 56.03 55.32 54.64 53.97 53.32 52.69 52.06 51.46 50.86 50.28 49.72 49.16 48.62 48.09 47.57 47.07 46.57 46.08 45.61 45.14 44.68 44.23 43.79 43.36 42.94 42.53 42.12 41.72 41.33 40.95 40.57 40.20 39.84 39.48 39.13 38.79 38.45 38.12 8.337 8.221 8.108 7.998 7.891 7.787 7.736 7.587 7.490 7.3% 7.305 7.215 7.128 7.043 6.%0 6.879 6.799 6.722 6.646 6.572 6.499 6.429 6.359 6.292 6.225 6.160 6.097 6.034 5.973 5.913 5.854 5.797 5.741 5.685 5.631 5.577 5.526 5.474 5.424 5.374 5.326 5.278 5.231 5.186 5.141 5.0% Values for Baume Scale Liquids Lighter Than Water Liquids Heavier Than Water Specific Gravity Weight Density, Lb/Ft3 Pounds per Gallon Specific Gravity Weight Density, Lb/Ft3 Pounds per Gallon SP SP 1.0000 0.9859 0.9722 0.9589 0.9459 0.9333 0.9211 0.9091 0.8974 0.8861 0.8750 0.8642 0.8537 0.8434 0.8333 0.8235 0.8140 0.8046 0.7955 0.7865 0.7778 0.7692 0.7609 0.7527 0.7447 0.7368 0.7292 0.7216 0.7143 0.7071 0.7000 0.6931 0.6863 0.67% 0.6731 0.6667 0.6604 0.6542 0.6482 0.6422 0.6364 0.6306 0.6250 0.6195 0.6140 0.6087 62.36 61.49 60.63 59.80 58.99 58.20 57.44 56.70 55.97 55.26 54.57 53.90 53.24 ' 52.60 51.97 51.36 50.76 50.18 49.61 49.05 48.51 47.97 47.45 46.94 46.44 45.95 45.48 45.00 44.55 44.10 43.66 43.22 42.80 42.38 41.98 41.58 41.19 40.80 40.42 40.05 39.69 39.33 38.98 38.63 38.29 37.% 8.337 8.219 8.105 7.994 7.886 7.781 7.679 7.579 7.482 7.387 7.295 7.205 7.117 7.031 6.947 6.865 6.786 6.708 6.632 6.557 6.484 6.413 6.344 6.275 6.209 6.143 6.079 6.016 5.955 5.895 5.836 5.778 5.722 5.666 5.612 5.558 5.506 5.454 5.404 5.354 5.306 5.257 5.211 5.165 5.119 5.075 1.0000 1.0140 1.0284 1.0432 1.0584 1.0741 1.0902 1.1069 1.1240 1.1417 1.1600 1.1789 1.1983 1.2185 1.2393 1.2609 1.2832 1.3063 1.3303 1.3551 1.3810 1.4078 1.4356 1.4646 1.4948 1.5263 1.5591 1.5934 1.6292 1.6667 1.7059 1.7470 1.7901 1.8354 1.8831 1.9333 62.36 63.24 64.14 65.06 66.01 66.99 67.99 69.03 70.10 71.20 72.34 73.52 74.73 75.99 77.29 78.64 80.03 81.47 82.96 84.51 86.13 87.80 89.53 91.34 93.22 95.19 97.23 99.37 101.60 103.94 106.39 108.95 111.64 114.46 117.44 120.57 8.337 8.454 8.574 8.697 8.824 8.955 9.089 9.228 9.371 9.518 9.671 9.828 9.990 10.159 10.332 10.512 10.698 10.891 11.091 11.297 11.513 11.737 11.%9 12.210 12.462 12.725 12.998 13.284 13.583 13.895 14.222 14.565 14.924 15.302 15.699 16.118 III SI *v - For Formulas, too page 7-3. / B-8 APPENDIX B-ENGINEERING DATA Steam Data CRANE Boiler Capacity The output of a steam generating plant is often expressed in pounds of steam delivered per hour. Since the steam out put may vary in temperature and pressure, the boiler capac ity is more completely expressed as the heat transferred in Btu per hour. Boiler capacity is usually expressed as kilo Btu (kB)/hour which is 1000 Btu/hour, or mega Btu (mB)/ hour which is 1,000,000 Btu/hour. The boiler capacity is: ----------- -- in kilo Btu/hour . 1000 hc -- hf = change in enthalpy, Btu/lb An older expression of boiler capacity in terms of an irra tional unit called "boiler horsepower" may be expressed: V (h,, - hr) _ #3310 970.3 X 34* 5 ~ That is, one boiler horsepower is equivalent to 34.5 pounds of water evaporated per hour at Standard Atmospheric Pressure and a temperature of 212 F. 1 boiler horsepower = horsepower/13.1547 horsepower = 550 ft-lb/sec. 1 Btu = 778.2 ft-lb 1 Btu = 252 calories 1 kw-hr = 3412.20 Btu . Horsepower of an Engine P = Mean effective pressure per square inch of the steam on the piston L = Length of stroke, in feet A = Area of piston, in square inches N = Number of strokes per minute then, Horsepower = PLAN 33000 The approximate mean effective pressure in the cylinder when the valve cuts off at: 14 stroke, equals steam pressure x .597 yz stroke, equals steam pressure x .670 stroke, equals steam pressure x .743 Y<i stroke, equals steam pressure x .847 h/% stroke, equals steam pressure x .919 % stroke, equals steam pressure x .937 y stroke, equals steam pressure x .966 y% stroke, equals steam pressure x .992 w is a s s n s s s n n in s t Ranges in Steam Consumption by Prime Movers (For Estimating Purposes) Simple Non-Condensing Engines........................... 29 to 45 pounds per H. P. hour Simple Non-Condensing Automatic Engines.... 26 to 40 pounds per H. P. hour Simple Non-Condensing Corliss Engines.............. 26 to 3 5 pounds per H. P. hour Compound Non-Condensing Engines..................... 19 to 28 pounds per H. P. hour Compound Condensing Engines............................. 12 to 22 pounds per H. P. hour Simple Duplex Steam Pumps................................... 120 to 200 pounds per H. P. hour Turbines, Non-Condensing...................................... 21 to 45 pounds per H. P. hour Turbines, Condensing................................................ 9 to 32 pounds per H. P. hour Quality of Steam... x = ----100 hf. where, hf = heat of liquid, in Btu/lb hf,, = latent heat of evaporation, in Btu/lb ha -- total heat of steam, in Btu/lb I 8 I I BBBBBBBBB 8 BBBBBBBBBBIlBBBBSa- CRANE APPENDIX 1-ENGINEERING DATA Power Required for Pumping B-9 Gals. per Min. Theoretical Horsepower Required to Raise Water (at 60 F) To Different Heights 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 feet feet feet feet feet feet feet feet feet feet feet feet feet feet feet 5 0.006 0.013 0.019 0.025 0.032 0.038 0.044 0.051 0.057 0.063 0.076 0.088 0.101 0.114 0.126 10 0.013 0.025 0.038 0.051 0.063 0.076 0.088 0.101 0.114 0.126 0.1521 0.177 0.202 0.227 0.253 15 0.019 0.038 0.057 0.076 0.095 0.114 0.133 0.152 0.171 0.190 0.227 0.265 0.303 0.341 0.379 20 0.025 0.051 0.076 0.101 0.126 0.152 0.177 0.202 0.227 0.253 0.303 0.354 0.404 0.455 0.505 25 0.032 0.063 0.095 0.126 0.158 0.1% 0.221 0.253 0.284 0.316 0.379 0.442 0.505 0.568 0.632 30 0.038 0.076 0.114 0.152 0.1% 0.227 0.265 0.303 0.341 0.379 0.455 0.531 0:606 0.682 0.758 35 0.044 0.088 0.133 0.177 0.221 0.265 0.310 0.354 0.398 0.442 0.531 0.619 0.707 0.7% 0.884 40 0.051 0.101 0.152 0.202 0.253 0.303 0.354 0.404 0.455 0.505 0.606 0.707 0.808 0.910 1.011 45 0.057 0.114 0.171 0.227 0.284 0.341 0.398 0.455 0.512 0.568 0.682 0.7% 0.910 1.023 1.137 50 0.063 0.126 0.190 0.253 0.316 0.379 0.442 0.505 0.568 0.632 0.758 0.884 1.011 1.137 1.263 60 0.076 0.152 0.227 0.303 0.379 0.455 0.531 0.606 0.682 0.758 0.910 1.061 1.213 1.364 1.516 70 0.088 0.177 0.265 0.354 0.442 0.531 0.619 0.707 0.796 0.884 1.061 .1.238 1.415 1.592 1.768 80 0.101 0.202 0.303 0.404 0.505 0.606 0.707 0.808 0.910 1.011 1.213 1.415 1.617 1.819 2.021 % 0.114 0.227 0.341 0.455 0.568 0.682 0.7% 0.910 1.023 1.137 1.364 1.592 1.819 2.046 2.274 100 0.126 0.253 0.379 0.505 0.632 0.758 0.884 1.011 1.137 1.263 1.516 1.768 2.021 2.274 2.526 125 0.158 0.316 0.474 0.632 0.7% 0.947 1.105 1.263 1.421 1.579 1.895 2.211 2.526 2.842 3.158 150 0.190 0.379 0.568 0.758 0.947 1.137 1.326 1.516 1.705 1.895 2.274 2.653 3.032 3.411 3.790 175 0.221 0.442 0.663 0.884 1.105 1.326 1.547 1.768 1.990 2.211 2.653 3.095 3.537 3.979 4.421 200 0.253 0.505 0.758 1.011 1.263 1.516 1.768 2.021 2.274 2.526 3.032 3.537 4.042 4.548 5.053 250 0.316 0.632 0.947 1.263 1.579 1.895 2.211 2.526 2.842 3.158 3.790 4.421 5.053 5.684 6.316 300 350 400 500 Gals. per Min. 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 125 150 175 200 250 300 350 400 500 0.379 0.442 0.505 0.632 0.758 0.884 1.011 1.263 1.137 1.326 1.516 1.895 1.516 1.768 2.021 2.526 1.895 2.211 2.526 3.158 2.274 2.653 3.032 3.7% 2.653 3.095 3.537 4.421 3.032 3.537 4.042 5.053 125 150 175 200 250 300 350 400 feet feet feet feet feet feet feet feet 0.158 0.316 0.474 0.632 0.190 0.379 0.568 0.758 0.221 0.442 0.663 0.884 0.253 0.505 0.758 1.011 0.316 0.632 0.947 1.263 0.379 0.758 1.137 1.516 0.442 0.884 1.326 1.768 0.505 1.011 1.516 2.021 0.790 0.947 1.105 1.263 0.947 1.137 1.326 1.516 1.105 1.326 1.547 1.768 1.263 1.516 1.768 2.021 1.579 1.895 2.211 2.526 1.895 2.274 2.653 3.032 2.211 2.653 3.095 3.537 2.526 3.032 3.537 4.042 1.421 1.579 1.895 2.211 1.705 1.895 2.274 2.653 1.990 2.211 2.653 3.095 2.274 2.526 3.032 3.537 2.842 3.158 3.7% 4.421 3.411 3.7% 4.548 5.305 3.979 4.421 5.305 6.1% 4.548 5.053 6.063 7.074 2.526 2.842 3.158 3.948 3.032 3.411 3.790 4.737 3.537 3.979 4.421 5.527 4.042 4.548 5.053 6.316 5.053 6.063 7.074 8.084 5.684 6.821 7.958 9.095 6.316 7.579 8.842 10.11 7.895 9.474 11.05 12.63 4.737 5.527 6.316 7.895 5.684 6.632 7.579 9.474 11.37 6.632 7.737 8.842 11.05 13.26 7.579 8.842 10.11 12.63 15.16 9.474 11.05 12.63 15.79 18.95 13.26 15.47 17.68 22.11 15.16 17.68 20.21 25.26 9.474 11.37 11.05 13.26 12.63 15.16 15.79 18.95 13.26 15.47 17.68 22.11 15.16 17.68 20.21 25.26 18.95 22.11 25.26 31.58 22.74 26.53 30.32 37.% 26.53 30.95 35.37 44.21 30.32 35.37 40.42 50.53 Spodflc gravity of voter.................. .................. PB* 4-6 Sptctflc gravity of llquidt offitr than water... .pag* A-7 3.411 3.979 4.548 5.684 3.790 4.421 5.053 6.316 4.548 5.305 6.063 7.579 5.305 6.063 6.821 7.579 6.190 7.074 7.958 8.842 7.074 8.084 9.095 10.11 8.842 10.11 11.37 12.63 HORSEPOWER = 33000 ... ft-lb/min = 550 .. .ft-lb/sec = 2544.48 .. .Btu/hr = 745.7 ...watts (whp) = QHp h- 247 000 = QP -*- 1714 (bhp) -- (whp) -T- e, = QHp 4- 247 000 ep (e,,) = QHp 4- 247 000 (bhp) where: (.u/hp) = water horsepower H = pump head in feet . (bhp) -- brake horsepower ep = pump efficiency Overall efficiency (e,,) takes into account all losses in the pump and driver. &q ~ &p eD dj* where: eD =* driver efficiency eT = transmission efficiency ey =* volumetric efficiency _ actual pump displacement (Q) (100) m /o) -- theoretical pump displacement (Q) Note: For fluids other than water, multiply table values by specific gravity. In pumping liquids with a viscosity considerably higher than that of water, the pump capacity and head are reduced. To calculate the horse power for such fluids, pipe friction head must be added to the elevation head to obtain the total head; this value is inserted in the first horsepower equation given above. B-10 APPENDIX B-ENGINEERING DATA Equivalents CRANE W W H I W H SD8 fl U i l l i Measure in. = 25.4 mm in. = 2.54 cm mm = mm micron = 0.03937 in. 0.00328 ft 0.000001 meter ft = 304.8 mm ft 30.48 cm 1 sq in. 1 sq cm 1 sq cm 1 sq ft = 6.4516 sq cm = 0.155 sq in. = 0.00108 sq ft = 929.03 sq cm Circumference of a circle = 2jrr Area of a circle = itr* rd xdJ 4 Weight 1 kg = 2.205 lb 1 cu in. of water (60 F) = 0.073551 cu in. of mercury (32 F) 1 cu in. of mercury (32 F) = 13.596 cu in. of water (60 F) 1 cu in. of mercury (32 F) = 0.4905 lb Velocity 1 ft per sec = 0.3048 m per sec 1 m per sec = 3.2808 ft per sec Density 1 lb per cu in. 1 gr per cu cm 1 lb per cu ft 1 kg per cu m 27.68 gram per cu cm 0.03613 lb per cu in. 16.0184 kg per cu m 0.06243 lb per cu ft Physical Constants ' Base of Natural Logarithms (e)................................................................... 2.7182818285 Acceleration of Gravity (g)...................... 32.174 ft/sec2................... (980.665 cm/secJ) Pi (,r)................................................................................................................. 3.1415926536 Degrees Kelvin Absolute Zero............................................ . 0 Water Freezing Point (14.696 psia).... ... 273.16 Water Boiling Point (14.6% psia)---- .... 373.16 Degrees Rankine 0 459.69 671.69 Degrees Centigrade - 273.16 0 100 Degrees Fahrenheit - 459.69 32 212 Equivalents of Temperature To convert degrees Centigrade to degrees Fahrenheit: t = 1.8 tc + 32 To convert degrees Fahrenheit to degrees Centigrade: t-- 32 1. Where: tc = temperature, in degrees Centigrade Prefixes Micro............... ........... one-millionth.............. ............. Milli................. ............. Centi................ ........... 0.000 001 ............ ............. 10-* 0.001 ............ ............. 10- 0.01 ............ ............. 10 Deci.................. ......... 0.1 ........... ............. 10-' Unity............... ........... one................................. ........... 1.0 ........... ............. 10" Deka................. ........... ten................................. ........... 10.0 ........... ............. 10' Hecto............... Kilo.................. Mega................ ........... 100.0 ........... 1000.0 ___ 1 000 000.0 ....... ............. 10* ... ............. 10 . ............. 10 Unity is not a prefix  CRANE AWNDIX b-engineering DATA Equivalents of Liquid Measures and Weights B-ll Liquid Measure or Weight U.S. Gallon Imperial Gallon U.S. Pint U.S. U.S. U.S. Pound Cubic Foot Cubic Inch Water* Liter Cubic Meter U.S. Gallon 1 0.833 3 8.337 0.13368 231 3.78533 0.003785 Imperial Gallon 1.2009 1 9.60752 10. 0.16054 277.42 4.545% 0.004546 U.S. Pint 0.125 0.1501 1 1.042 0.01671 28.875 0.473166 0.000473 U.S. Pound Water* 0.11995 0.09992 0.095% 1 0.016035 27.708 0.45405 0.000454 U.S. Cubic Foot 7.48052 6.22888 59.8442 62.365 1 1728 28.31702 0.028317 U.S. Cubic Inch 0.004329 0.00361 0.034632 0.03609 0.0005787 1 0.016387 0.0000164 Liter 0.2641779 0.2199756 2.113423 2.202 0.0353154 61.02509 1 0.001000 Cubic Meter 264.170 219.969 2113.34 2202. 35.31446 61023.38 999.972 1 Water at 60 F. 1 Barrel = 42 gallons (petroleum measure) Problem: . Solution : How many British Imperial Gallons are equivalent The Imperial Gallon equivalent of l U.S. Gallon is to to U.S. Gallons? 0-833. Then, 10 x 0.833 = 8.33 Imperial Gallons. B B Ull Bll BBfl B-H Equivalents of Pressure and Head Pressure or Head lb/in.* lb/ft* Atmos kg/cm* pheres kg/m* in. water (60 F) ft water (60 F) in. mm mercury mercury (32 F) (32 F) lb/in.* 1 144 0.068046 0.070307 703.067 27.707 2.3039 2.03601 51.7148 lb/ft* 0.0069445 1 0.000473 0.000488 4.88241 0.19241 0.01603 0.014139 0.35913 Atmospheres 14.6% 2116.22 1 1.0332 10332.27 407.17 33.931 29.921 760. kg/cm* 14.2234 2048.17 0.%784 1 10000. 394.08 32.840 28.959 735.559 kg/m* 0.0014Z2 0.204817 0.0000968 0.0001 1 0.03941 0.003284 0.0028% 0.073556 in. water* 0.036092 5.1972 0.002456 0.00253 25.375 1 0.08333 0.073483 1.8665 ft water* 0.433103 62.3668 0.029471 0.03045 304.50 12. 1 0.88180 22.3980 in. mercuryf 0.491157 70.7266 0.033421 0.03453 345.316 13.608 1.1340 1 25.40005 mm mercuryf 0.0193368 2.78450 0.0013158 0.0013595 13.59509 0.535764 0.044647 0.03937 . 1 Water at 60 F. fMercury at 32 F. Problem: Solution: How many inches of mercury are equivalent to 10 1 inch of water is equal to 0.073483 inch mercury, inches of water? Then, 10 x 0.073483 = 0.73483 inch mercury. To convert fiom on0 tot of units to another, locate the given unit in the left hand column, and multiply the numerical value by the fac tor shown horizontally to the right, under the set of units desired. B-12 APPENDIX B-ENGINEERING DATA Four-Place Logarithms to Base 10 CRANE The logarithms to base 10 of numbers between 1 and 10, correct to four places, are given in the tables shown on this and the following page. If the decimal point in the number is moved n places to the right (or left), the value of n (or -- n) is added to the logarithm, thus: log 3.14 =0.4969 log 314. =0.4969 +2 or 2.4969 _ log .0314 = 0.4969 -- 2, which may be written 2.4969 or 8.4969-10 If the given number has more than four significant figures, it should be reduced to four figures, since those beyond four figures will not affect the result in four-place computations. The logarithm of a number having four significant figures must be interpolated by adding to the loga rithm of the three figure number, the amount under the fourth figure, as read in the proportional parts section of the table. Thus, the logarithm of 3.1416 is found as follows: a. Reduce the number to four significant figures: 3.142 b. The log of 3.14 is .4969 c. The value of the proportional part under 2 (the fourth figure) is 3 d. Then, the log 3.142 =0.4969+.0003 or 0.4972 Natural logarithms: Many calculations make use of natural logarithms (Base e -- 2.7183). To con vert base 10 (common) logarithms to natural loga rithms, multiply the value for the former by 2.30258. Natural logarithms are also called Hyperbolic or Naperian logarithms. log aft=log a+log b log |=log a--log b log an = n log a , log a log Va=-jj-- Proportional Parts N 0123456789 123456789 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 . 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 0000 0414 0792 1139 1461 1761 2041 2304 2553 2788 3010 3222 3424 3617 3802 3979 4150 4314 4472 4624 4771 4914 5051 5185 5315 5441 5563 5682 5798 5911 0043 0453 0828 1173 1492 1790 2068 2330 2577 2810 3032 3243 3444 3636 3820 3997 4166 4330 4487 4639 4786 4928 5065 5198 5328 5453 5575 5694 5809 5922 0086 0492 0864 1206 1523 1818 2095 2355 2601 2833 3054 3263 3464 3655 3838 4014 4183 4346 4502 4654 4800 4942 5079 5211 5340 5465 5587 5705 5821 5933 0128 0531 0899 1239 1553 1847 2122 2380 2625 2856 3075 3284 3483 3674 3856 4031 4200 4362 4518 4669 4814 4955 5092 5224 5353 5478 5599 5717 5832 5944 0170 0569 0934 1271 1584 1875 2148 2405 2648 2878 30% 3304 3502 3692 3874 4048 4216 4378 4533 4683 4829 4969 5105 5237 5366 5490 5611 5729 5843 5955 0212 0607 0%9 1303 1614 1903 2175 2430 2672 2900 3118 3324 3522 3711 3892 4065 4232 4393 4548 4698 4843 4983 5119 5250 5378 5502 5623 5740 5855 5%6 0253 0645 1004 1335 1644 1931 2201 2455 2695 2923 3139 3345 3541 3729 3909 4082 4249 4409 4564 4713 4857 4997 5132 5263 5391 5514 5635 5752 5866 5977 0294 0682 1038 1367 1673 0334 0719 1072 1399 1703 1959 2227 2480 2718 2945 1987 2253 2504 2742 2%7 3160 3365 3560 3747 3927 3181 3385 3579 3766 3945 4099 4265 4425 4579 4728 4116 4281 4440 4594 4742 4871 5011 5145 5276 5403 4886 5024 5159 5289 5416 5527 5647 5763 5877 5988 5539 5658 5775 5888 5999 0374 0755 1106 1430 1732 2014 2279 2529 2765 2989 3201 3404 3598 3784 3%2 4133 4298 4456 4609 4757 4900 5038 5172 5302 5428 5551 5670 5786 5899 6010 4 8 12 17 21 25 29 33 37 4 8 11 15 19 23 26 30 34 3 7 10 14 17 21 24 28 31 3 6 10 13 16 19 23 26 29 3 6 9 12 15 18 21 24 27 3 6 8 11 14 17 20 22 25 3 5 8 11 13 16 18 21 24 2 5 7 10 12 15 17 20 22 2 5 7 9 12 14 16 19 21 2 4 7 9 11 13 16 18 20 2 4 6 8 11 13 15 17 19 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 15 17 2 4 6 7 9 11 13 15 17 2 4 5 7 9 11 12 14 16 2 3 '5 7 9 10 12 14 15 2 3 5 7 8 10 11 13 15 2 3 5 6 8 9 11 13 14 2 3 5 6 8 9 11 12 14 1 3 4 6 7 9 10 12 13 1 3 4 6 7 9 10 11 13 1 3 4 6 7 8 10 11 12 1 3 4 5 7 8 9 11 12 1 3 4 5 6 8 9 10 12 1 3 4 5 6 8 9 10 11 1 2 4 5 6 7 9 10 11 1 2 4 5 b 7 8 10 11 1 2 3 S 6 7 8 9 10 1 2 3 5 6 7 8 9 10 1 2 3 4 b 7 8 9 10 N 0 1 2 3 4 5 6 7 8 9 123456789 fg g g g g g m i BII m B 8 fl g ff g H I r2 0 CRANE appendix -engineering oata B-13 Four-Place Logarithms to Base 10 " continued I 1 Proportional Parts N o 1 2 34 5| 6 7 8 9 i 123456789 4.0 4.1 4.2 4.3 4.4 6021 6128 6232 6335 6435 6031 6138 6243 6345 6444 6042 6149 6253 6355 6454 6053 6160 6263 6365 6464 6064 6170 6274 6375 6474 6075 6180 6284 6385 6484 6085 6191 6294 6395 6493 60% 6201 6304 6405 6503 6107 6232 6314 6415 6513 6117 i 6222 ! 6325 l 6425 6522 1 2 3 4 5 6 8 9 10 1 23456789 1 23456789 123456789 123456789 4.5 4.6 4.7 4.8 6532 6628 6721 6812 6542 6637 6730 6821 6551 6646 6739 6830 6561 6656 6749 6839 6571 6665 6758 6848 6580 6675 6767 6857 6590 6684 6776 6866 6599 6693 6785 6875 6609 6702 6794 6884 6618 6712 6803 6893 1 23456789 1 23456778 1 23455678 1 2344567 8 4.9 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 1 2 3 4 4 5 6 7 8 5.0 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 1 2 3 3 4 5 6 7 8 5.1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 1 2 3 3 4 5 6 7 8 5.2 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 1 2 2 3 4 5 6 7 7 5.3 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 1 2 2 3 4 5 6 6 7 5.4 7324 7332 7340 7348 7356 7364 7372 7380 7388 73% 1 2 2 3 4 5 6 6 7 5.5 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 1 2 2 3 4 5 5 6 7 5.6 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 1 2 2 3 4 5 5 6 7 5.7 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 1 2 2 3 4 5 5 6 7 5.8 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 1 1 2 3 4 4 5 6 7 5.9 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 1 1 2 3 4 4 5 6 7 6.0 7782 7789 77% 7803 7810 7818 7825 7832 7839 7846 1 1 2 3 4 4 5 6 6 6.1 7853 7860 7868 7875 7882 7889 78% 7903 7910 7917 1 1 2 3 4 4 5 6 6 6.2 7924 7931 7938 7945 7952 7959 7%6 7973 7980 7987 1 1 2 3 3 4 5 6 6 6.3 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 1 1 2 3 3 4 5 5 6 6.4 8062 8069 8075 8082 8089 80% 8102 8109 8116 8122 1 1 2 3 3 4 5 5 6 6.5 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 1 1 2 3 3 4 5 5 6 6.6 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 1 1 2 3 3 4 5 5 6 6.7 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 1 1 2 3 3 4 5 5 6 6.8 8325 8331 8338 8344 8351 .8357 8363 8370 8376 8382 1 1 2 3 3 4 4 5 6 6.9 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 1 1 2 2 3 4 4 5 6 7.0 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 1 1 2 2 3 4 4 5 6 7.1 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 1 1. 2 2 3 4 4 5 5 7.2 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 1 1 2 2 3 4 4 5 5 7.3 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 1 1 2 2 3 4 4 5 5 7.4 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 1 1 2 2 3 4 4 5 5 7.5 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 1 1 2 2 3 3 4 5- 5 7.6 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 1 1 2 2 3 3 4 5 5 7.7 8865 8871 8876 8882. 8887 8893 8899 8904 8910 8915 1 1 2 2 3 3 4 4 5 7.8 8921 8927 8932 8938 8943 8949 8954 8960 8%5 8971 1 1 2 2 3 3 4 4 5 7.9 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 1 1 2 2 3 3 4 4 5 8.0 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 1 1 2 2 3 3 4 4 5 8.1 9085 9090 90% 9101 9106 9112 9117 9122 9128 9133 1 1 2 2 3 3 4 4 5 8.2 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 1 1 2 2 3 3 4 4 5 8.3 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 1 .1 2 2 3 3 4 4 5 8.4 9243' 9248 9253 9258 9263 9269 9274 9279 9284 9289 1 1 2 2 3 3 4 4 5 8.5 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 1 1 2 2 3 3 4 4 5 8.6 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 1 1. 2 2 3 3 4 4 5 8.7 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 0 1 1 2 2 3 3 4 4 8.8 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 0 1 1. 2 2 3 3 4 4 8.9 9494 9499 9504. 9509 9513 9518 9523 9528 9533 9538 0 1 1 2 2 3 3 4 4 9.0 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 0 1 1 2 2 3 3 4 4 9.1 9590 9595 %00 %05 %09 %14 %19 %24 %28 %33 0 1 1 2 2 3 3 4 4 9.2 9638 9643 9647 %52 %57 %61 %66 %71 %75 9680 0 1 1 2 2 3 3 4 4 9.3 9685 9689 %94 %99 9703 9708 9713 9717 9722 9727 0 1 1 2 2 3 3 4 4 9.4 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 0 1 1 2 2 3 3 4 4 9.5 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 0 1 1 2 2 3 3 4 4 9.6 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 0 1 1 2 2 3 3 4 4 9.7 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 0 1 1 2 2 3 3 4 4 9.8 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 0 1 1 2 2 3 3 4 4 9.9 9956- 9961 9%5 9%9 9974 9978 9983 9987 9991 99% 0 1 1 2 2 3 3 3 4 N 0 12 3 4 5 6 7 8 9 123456789 " ^jmsn iw.nvT' SVSSJK'- B-14 APPENDIX 8-ENGINEERING DATA CRANE Flow of Water Through Schedule 40 Steel Pipe Disc harge Gallons per Minute Cubic Ft. per Second Pressure Drop per 100 feet and Velocity in Schedule 40 Pipe for Water at 60 F. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Veloc- Press, ity Drop Feet Lbs. per per Second Sq. In. Vs' V*' %' .2 .3 .4 .5 .6 .8 0^000446 01000668 0.000891 0.00111 0.00134 0.00178 1.13 1.69 2.26 2.82 3.39 4.52 1.86 4.22 6.98 10.5 14.7 25.0 0.616 0.924 1.23 1.54 1.85 2.46 0.359 0.903 0.504 1.61 0.672 2.39 0.840 3.29 1.01 5.44 1.34 0.159 0.317 0.345 0.422 0.539 0.528 0.751 0.633 1.25 0.844 0.061 /k 0.086 0.167 0.301 0.033 0.240 0.361 0.041 0.408 0.481 0.102 1 llA 1 2 3 4 S 0.00223 0.00446 0.00668 0.00891 0.01114 5.65 37.2 n.29 134.4 2' 3.08 8.28 6.16 30.1 9.25 64.1 12.33 111,2 1.68 3.36 5.04 6.72 8.40 1.85 6.58 13.9 23.9 36.7 1.06 2.11 3.17 4.22 5.28 0.600 0.602 2.10 1.20 4.33 1.81 7.42 2.41 11.2 3.01 0.155 0.371 0.526 0.743 1.09 1.114 1.83 1.49 2.75 1.86 0.048 0.164 0.429 0.336 0.644 0.565 0.858 0.835 1.073 w 0.044 0.090 0.473 0.043 0.150 0.630 0.071 0.223 0.788 0.104 6 8 11) 15 20 0.01337 0.01782 0.02228 0.03342 0.04456 0.574 0.765 0.956 1.43 1.91 0.044 IVi' 10.08 51.9 6.33 15.8 0.073 13.44 91.1 8.45 27.7 0.108 0.670 0.046 10.56 42.4 0.224 1.01 0.094 3 0.375 1.34 0.158 0.868 0.056 i'K 3.61 4.81 6.02 9.03 12.03 3.84 6.60 9.99 21.6 37.8 2.23 2.97 3.71 5.57 7.43 1.17 1.99 2.99 6.36 10.9 1.29 1.72 2.15 3,22 4.29 0.309 0.946 u.616 1.26 0.774 1.58 1*63 2.37 2.78 3.16 0.145 0.241 0.361 0.755 1.28 25 30 35 40 45 0.05570 0.06684 0.07798 0.08912 0.1003 2.39 2.87 3.35 3.83 4.30 0.561 1.68 0.786 2.01 1.05 2.35 1.35 2.68 1.67 3.02 0.234 1.09 0.327 1.30 0.436 1.52 0.556 1.74 0.668 1.95 0.083 0.812 0.114 0.974 0.151 1.14 0.192 1.30 0.239 1.46 0.041 4r 9.28 0.056 11.14 0.704 0.882 0.041 12.99 0.095 1.01 0.052 14.85 0.117 1.13 0.064 16.7 23.6 32.2 41.5 5.37 6.44 7.51 8.59 9.67 4.22 5.92 7.90 10.24 12.80 3.94 4.73 5.52 6.30 7.09 1.93 2.72 3.64 4.65 5.85 50 0.1114 60 0.1337 70 0.1560 80 0.1782 90 0.2005 4.78 5.74 6.70 7.65 8.60 2.03 2.87 3.84 4.97 6.20 3.35 4.02 4.69 5.36 6.03 0.839 2.17 1.18 2.60 1.59 3.04 2.03 3.47 2.53 3.91 0.288 1.62 0.406 1.95 0.540 2.27 0.687 2.60 0.861 2.92 0.142 1.26 0.204 1.51 0.261 1.76 0.334 2.02 0.416 2.27 0.076 0.107 0.143 0.180 0.224 5jp 10.74 15.66 12.89 22.2 1.12 0.047 1.28 0.060 1.44 0.074 b 7.88 9.47 11.05 12.62 14.20 7.15 10.21 13.71 17.59 22.0 100 125 150 175 200 225 iso 275 325 ASA .175 400 47.5 450 475 500 550 500 650 700 750 800 850 900 950 1 boo 1 100 1 200 1300 0.2228 0.2785 0.3342 0.3899 0.4456 0.5013 0.557 0.6127 0.6684 0.7241 0.7798 0.8355 0.8912 0.0469 1.003 1.059 1.114 1.225 1.337 1.448 1.560 1.671 1.782 1.894 2.005 2.117 2.228 2.451 2.674 2.896 9.56 11,97 14.36 16.75 19.14 7.59 6.70 11.76 8.38 16.70 10.05 22.3 11.73 28.8 13.42 3.09 4.71 6.69 8.97 11.68 4.34 5.43 6.51 7.60 8.68 1.05 1.61 2.24 3.00 3.87 3.25 4.06 4.87 5.68 6.49 0.509 2.52 0.769 3.15 1.08 3.78 1.44 4.41 1.85 5.04 15.09 14.63 9.77 10.85 11.94 13.00 14.12 4.83 7.30 5.93 8.12 7.14 8.93 8.36 9.74 9.89 10.53 2.32 2.84 3.40 4.02 4.09 5.67 6.30 6.93 7.56 8.19 11.36 5.41 8.82 12.17 6.18 9.45 12.98 7.03 10.08 13.80 7.89 10.71 10' 14.61 8.80 11.34 1.93 2.03 2.24 2.44 2.64 0.054 0.059 0.071 0.083 0.097 12' 11.97 12.60 13.85 15.12 2.85 3.05 3.25 3.46 3.66 0.112 2.01 0.127 2.15 0.142 2.29 0.16C 2.44 0.179 2.58 0.047 0.054 14' 0.061 0.068 2.02 0.042 0.075 2.13 0.047 3.86 4.07 4.48 4.88 5.29 0.198 2.72 0.2H 2.87 0.26C 3.15 0.306 3.44 0.355 3.73 0.083 2.25 0.091 2.37 0.110 2.61 0.128 2.85 0.150 3.08 0.052 0.057 lb' 0.068 0.080 2.18 0.042 0.093 2.36 0.048 0.272 1.60 0.415 2.01 0.580 2.41 0.774 2.81 0.985 3.21 1.23 1.46 1.79 2.11 2.47 3.61 4.01 4.41 4.81 5.21 2.84 3.25 3.68 4.12 4.60 5.62 6.02 6.42 6.82 7.22 5.12 7.62 5.65 8.02 6.79 ' -8.82 8.04 9.63 10.43 11.23 12.03 12.83 13.64 14.44 15.24 16.04 17.65 0.090 l.n 0.135 1.39 0.190 1:67 0.253 1.94 0.323 2.22 0.401 2.50 0.495 2.78 0.583 3.05 0.683 3.33 0.797 3.61 0.919 3.89 1.05 4.16 1.19 4.44 1.33 4.72 1.48 5.00 1.64 1.81 2.17 2.55 2.98 5.27 5.55 6.11 6.66 7.22 3.43 3.92 4.43 5.00 5.58 7.78 8.33 8.88 9.44 9.99 .6.21 6.84 8.23 10.55 11.10 12.22 13.33 14.43 0.036 15.78 6.055 19.72 0.077 0.102 0.130 0.162 1.44 0.195 1.60 0.234 1.76 0.275 1.92 0.320 2.08 0.367 2.24 0.416 2.40 0.471 2.56 0.529 2./3 0.590 2.89 0.653 3.04 0.720 3.21 0.861 3.53 1.02 3.85 1.18 4.17 1.35 1.55 1.75 1.96 2.18 4.49 4.81 5.13 5.45 5.77 2.42 2.68 3.22 3.61 4.45 6.09 6.41 7.05 7.70 8.33 26.9 41.4 0.043 0.051 0.061 u.u/2 0.083 0.095 0.108 0.121 0.136 6.151 0.166 u. 182 6.258 6*301 0.343 6.392 0.613 1400 1500 1 600 1 800 2 000 2 500 3 000 3 500 4000 4500 3.119 3.342 3.565 4.010 4.456 5.570 6.684 7.798 8.912 10.03 5.70 6.10 6.51 7.32 8.14 10.17 12.20 14.24 16.27 18.31 0.409 4.01 0.466 4.30 0.527 4.59 0.663 5.16 0.808 5.73 1.24 1.76 2.38 3.08 3.87 7.17 8.60 10.03 11.47 12.90 0.171 3.32 0.195 3.560.219 3.79 0.276 4.27 0.339 4.74 0.515 5.93 0.731 7.11 0.982 8.30 1.27 9.48 1.60 10.67 0.107 2.54 0.122 2.72 0.138 2.90 0.172 3.27 0.209 3.63 0.321 4.54 0.451 .5.45 0.607 6.35 0.787 7.26 0.990 8.17 0.055 0.063 lb 0.071 0.088 2.58 0.050 0.107 2.87 0.060 0.163 3.59 0.232 4.30 0.312 5.02 0.401 5.74 0.503 6.46 0.091 0.129 3.46 0.173 4.04 0.222 4.62 0.280 5.20 15.55 16.66 17.77 19.99 22.21 0.075 0.101 0.129 3.19 0.162 3.59 5.13 d.9l> 6.61 8.37 10.3 8.98 9.62 12.82 16.03 0.052 0.065 l.M 1.46 3.94 14*4 5 000 6000 7000 8 000 9000 11.14 13.37 15.60 17.82 20.05 20.35 24.41 28.49 4.71 14.33 6.74 17.20 9.11 20.07 22.93 25.79 1.95 11.85 2.77 14.23 3.74 16.60 4.84 18.% 6.09 21.34 1.21 1.71 2.31 2.99 3.76 9.08 10.89 12.71 14.52 16.34 0.617 7.17 0.877 8.61 1.18 10.04 1.51 11.47 1.90 12.91 0.340 5.77 0.483 6.93 0.652 8.08 0.839 9.23 1.05 10.39 0.199 0.280 0.37b 0.488 0.608 3.99 4.79 b. jo 7.18 0.079 0. Ill 10 000 12 000 14 000 16 000 18 000 20 000 22.28 26.74 31.19 35.65 40.10 44.56 28.66 7.46 23.71 34.40 10.7 28.45 33.19 4.61 18.15 6.59 21.79 8.89 25.42 29.05 32.68 36.31 2.34 14.34 3.33 17.21 4.49 20.08 5.83 22.95 7.31 25.82 9.03 28.69 For pipe lengths other than 100 feet, the pressure drop is proportional to the length. Thus, for 50 feet of pipe, the pressure drop is approximately one-half the value given in the table ... for 300 feet, three times the given value, etc. 1.28 11.54 1.83 13.85 2.45 16.16 3.18 18.47 4.03 20.77 4.93 23.08 0.739 7.98 1.06 9.58 1.43 11.17 1.85 12.77 2.32 14.36 2.86 15.96 0.294 0.723 0.907 1.12 Velocity is a function of the cross sectional flow area; thus, it is constant for a given -flow rate and is independent of pipe lengtn. For calculation! for pipe other than Schedule 40, tee explanation on next page. lt llS B H -H IB H i H W H 8 8i C F 1 S F c t t CRANE AffiNDIX (-ENGINEERING DATA Flow of Air Through Schedule 40 Steel Pipe B-15 For lengths of pipe other than 100 feet, the pressure drop is proportional to the length. Thus, for 50 feet of pipe, the pressure drop is approximately one-half the value given in the table . . . for 300 feet, three times the given value, etc. Free Air Com <l'm pressed Air Cubic Feet Cubic Feet Per Minute Per Minute at 60 F and at 60 F and 14.7 psia 100 psig Pressure Drop of Air In Pounds per Square Inch Per 100 Feet of Schedule 40 Pipe For Air at 100 Pounds per Square Inch Gauge Pressure and 60 F Temperature The pressure drop is also in versely proportional to the absolute pressure and directly proportional to the absolute temperature. Therefore, to determine the pressure drop for inlet or aver age pressures other than 100 psi and at temperatures other than 60 F, multiply the values given in the table by the ratio: /100+14.7\/460 + ('\ \ P+14.7 A 520 ) Vi Vi' W W 1 2 3 0.128 0.256 0.384 0.361 1.31 3.06 0.083 0.285 0.605 0.018 0.064 0.133 0.020 0.042 % 4s 0.513 0.641 4.83 7.45 1.04 1.58 0.226 0.071 0.343 0.106 0.027 1' 6 0.769 10.6 2.23 0.408 0.148 0.037 8 1.025 18.6 3.89 0.848 0.255 0.062 0.019 10 15 1.282 28.7 1.922 5.96 13.0 1.26 2.73 0.356 0.834 0.094 0.201 0.029 0.062 iy' Wz' 20 2.563 22.8 4.76 1.43 0.345 0.102 0.026 25 3.204 30 3.845 4350 4.486 5.126 45 5.767 35.6 7.34 10.5 14.2 18.4 23.1 2.21 3.15 4.24 5.49 6.90 0.526 0.748 1.00 1.30 1.62 0.156 0.219 0.293 0.379 0.474 0.039 0.055 0.073 0.095 0.116 0.019 0.026 0.035 0.044 0.055 2' where: "P" is the inlet or average gauge pressure in pounds per square inch, and, "t" is the temperature in degrees Fahrenheit under consideration. The cubic feet per minute of compressed air at any pres sure is inversely proportional to the absolute pressure and directly proportional to the absolute temperature. To determine the cubic feet per minute of compressed air at any temperature and pres sure other than standard con ditions, multiply the value of cubic feet per minute of free air by the ratio: ( 14.7 \/460 + t\ \14.7 + P/\ 520 ) 50 60 70 80 90 100 ` 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 550 600 650 700 750 800 850 900 950 1000 1100 1200 1300 6.408 7.690 8.971 10.25 11.53 w 0.019 0.023 12.82 16.02 19.22 22.43 25.63 0.029 0.044 0.062 0.083 0.107 28.84 32.04 35.24 38.45 41.65 0.134 0.164 0.191 0.232 . 0.270 44.87 0.313 48.06 , 0.356 51.26 0.402 54.47 0.452 57.67 0.507 60.88 64.08 70.49 76.90 83.30 0.562 0.623 0.749 0.887 1.04 89.71 96.12 102.5 108.9 115.3 1.19 1.36 1.55 1.74 1.95 121.8 128.2 141.0 153.8 166.6 2.18 2.40 2.89 3.44 4.01 28.5 40.7 3' 0.021 0.028 0.036 V/z' 0.045 0.022 0.055 0,027 0.066 - 0.032 0.078 0.037 0.090 0.043 0.104 0.119 0.134 0.151 0.168 0.050 0.057 0.064 0.072 0.081 0.187 0.206 0.248 0.293 0.342 0.089 0.099 0.118 0.139 0.163 0.395 0.451 0.513 0.576 0.642 0.188 0.214 0.244 0.274 0.305 0.715 0.788 0.948 1.13 1.32 0.340 0.375 0.451 0.533 0.626 8.49 12.2 16.5 21.4 27.0 33.2 4# 0.030 0.034 0.038 0.042 0.047 0.052 0.062 0.073 0.086 0.099 0.113 0.127 0.144 0.160 0.178 0.197 0.236 0.279 0.327 1.99 2.85 3.83 4.96 6.25 7.69 11.9 17.0 23.1 30.0 37.9 5' 0.032 0.036 0.041 0.046 0.051 0.057 0.063 0.075 0.089 0.103 0.578 0.819 1.10 1.43 1.80 2.21 3,39 4.87 6.60 8.54 10.8 13.3 16.0 19.0 22.3 25.8 ' 29.6 33.6 37.9 6' 0.023 0.025 0.030 0.035 0.041 0.149 0.200 0.270 0.350 0.437 0.534 0.825 1.17 1.58 2.05 2.59 3.18 3.83 4.56 5.32 6.17 7.05 8.02 9.01 10.2 11.3 12.5 15.1 18.0 21.1 24.3 27.9 31.8 35.9 40.2 0.067 0.094 0.126 0.162 0.203 0.247 0.380 0.537 0.727 0.937 1.19 1.45 1.75 2.07 2.42 2.80 3.20 3.64 4.09 4.59 5.09 5.61 6.79 8.04 9.43 10.9 12.6 14.2 16.0 18.0 20.0. 22.1 26.7 31.8 37.3 0.019 0.027 0.036 0.046 0.058 0.070 0.107 0.151 0.205 0.264 0.331 0.404 0.484 0.573 0.673 0.776 0.887 1.00 1.13 1.26 1.40 1.55 1.87 2.21 2.60 3.00 3.44 3.90 4.40 4.91 5.47 6.06 7.29 8.63 10.1 2 Q B 0 "8 Calculation* for Pip* Other than Schedule 40 To determine the velocity of water, or the pressure drop of water or air, through pip other than Schedule 40, use the following formulas: 1400 1500 1600 1800 2000 2500 3 000 3500 4 000 .4500 5000 6000 7000 8000 9000 179.4 192.2 205.1 230.7 256.3 320.4 384.5 448.6 512.6 576.7 640.8 769.0 897.1 1025 1153 4.65 5.31 6.04 7.65 9.44 14.7 21.1 28.8 37.6 47.6 1.52 1.74 1.97 2.50 3.06 4.76 6.82 9,23 12.1 15.3 18.8 27.1 36.9 0.718 0.824 0.932 1.18 1.45 2.25 3.20 4.33 5.66 7.16 8.85 12.7 17.2 22.5 28.5 0.377 0.431 0.490 0.616 0.757 1.17 1.67 2.26 2.94 3.69 4.56 6.57 8.94 11.7 14.9 0.119 0.136 0.154 0.193 0.237 0.366 0.524 0.709 0.919 1.16 1.42 2.03 2.76 3.59 4.54 0.047 0.054 0.061 0.075 0.094 0.143 0.204 0.276 0.358 0.450 0.552 0.794 1.07 1.39 1.76 8' 0.023 0.035 0.051 0.068 0.088 0.111 0.136 0.195 0.262 0.339 0.427 10' 0.016 0.022 0.028 0.035 0.043 0.061 0.082 0.107 0.134 11.8 13.5 15.3 19.3 23.9 37.3 12 0.018 0.025 0.034 0.044 0.055 Subscript "a" refers to the 10000 11000 12 000 13 000 14000 ' 1282 1410 1538 1666 1794 35.2 18.4 22.2 26.4 31.0 36.0 5.60 6.78 8.07 9.47 11.0 2.16 2.62 3.09 3.63 4.21 0.526 0.633 0.753 0.884 1.02 0.164 0.197 0.234 0.273 0.316 0.067 0.081 0.096 0.112 0.129 Schedule of pipe through which velocity or pressure drop is desired. Subscript "40`` refers to the 15000 16000 18 000 20 000 22000 1922 2051 2307 2563 2820 12.6 14.3 18.2 22.4 27.1 4.84 5.50 6.96 8.60 10.4 1.17 1.33 1.68 2.01 2.50 0.364 0.411 0.520 0.642 0.771 0.148 0.167 0.213 0.260 0.314 i velocity or pressure drop through Schedule 40 pipe, as 24000 26 000 3076 3332 given in the tables on these 28000 3588 facing pages. 30000 3845 32.3 37.9 ... 12.4 14.5 16.9 19.3 2.97 3.49 4.04 4.64 0.918 1.12 1.25 1.42 0.371 0.435 0.505 0.520 (Pimciipiu 'T*1 -- B-16 APPENDIX E-ENGINEERING DATA CRANE Commercial Wrought Steel Pipe Data Schedule Wall Thickness--Per ASA B36.10-1950 Nominal Pipe Size Inches 14 4> 16 3Vo 1$ 20 24 ` & 30 8 10 8 12 4a) 14 *0 16 X 18 <2 20 24 30 8 10 ro 12 3 14 Tx45> 16 18 & 20 24 30 Vs Va. Vs Vi % 1 IV* i% 2 2Vi s 3 o m X4 c8 5 6 8 10 12 14 16 18 20 24 8 s 10 12 2o 14 16 1in 18 20 24 y8 aO V* % 0 % % <8 1 W* Outside Diam eter Inches Thick ness Inches Inside Diameter dD Inches Feet d* Inside Diameter Functions (In Inches) d> d* d* Transverse , Internal Area aA Sq. In. Sq. Ft. 14 0.250 13.5 1.125 182.25 2460.4 33215. 448400. 143.14 0.994 16 0.250 15.5 1.291 240.25 3723.9 57720. 894660. 188.69 1.310 18 0.250 17.5 1.4583 306.25 5359.4 93789. 1641309. 240.53 1.670 20 0.250 19.5 1.625 380.25 7414.9 144590. 2819500. 298.65 2.074 24 0.250 23.5 1.958 552.25 12977. 304980. 7167030. 433.74 3.012 30 0.312 29.376 2.448 862.95 25350. 744288. 21864218. 677.76 4.707 8.625 10.75 12.75 14 0.250 0.250 0.250 0.312 8.125 0.6771 66.02 10.25 0.8542 105.06 12.25 1.021 150.06 13.376 1.111 178.92 536.38 1076.9 1838.3 2393.2 4359.3 11038. 22518. 32012. 35409. 113141. 275855. 428185. - 51.85 0.3601 82.52 0.5731 117.86 0.8185 140.52 0.9758 16 0.312 15.376 1.281 236.42 3635.2 55894. 859442. 185.69 1.290 18 0.312 17.376 1.448 301.92 5246.3 91156. 1583978. 237.13 1.647 20 0.375 19.250 1.604 370.56 7133.3 137317. 2643352. 291.04 2.021 24 0.375 23.25 1.937 540.56 12568. 292205. 6793832. 424.56 2.948 30 0.500 29.00 2.417 841.0 24389. 707281. 20511149. 660.52 4.587 8.625 10.75 12.75 14 0.277 0.307 0.330 0.375 8.071 0.6726 65.14 10.136 0.8447 102.74 12.09 1.0075 146.17 13.25 1.1042 175.56 525.75 1041.4 1767.2 2326.2 4243.2 10555. 21366. 30821. 34248. 106987. 258304. 408394. 51.16 80.69 114.80 137.88 0.3553 0.5603 0.7972 0.9575 16 0.375 15.25 1.2708 232.56 3546.6 54084. 824801. 182.65 1.268 18 0.438 17.124 1.4270 293.23 5021.3 85984. 1472397. 230.30 1.599 20 0.500 19.00 1.5833 361.00 6859.0 130321. 2476099. 283.53 l.%9 24 0.562 22.876 1.9063 523.31 11971. 273853. 6264703. 411.00 2.854 30 0.625 28.75 2.3958 826.56 23764. 683201. 19642160. 649.18 4.508 0.405 0.540 0.675 0.068 0.088 0.091 0.269 0.0224 0.0724 0.364 0.0393 0.1325 0.493 0.0411 0.2430 0.0195 0.0482 0.1198 0.005242 0.01756 0.05905 0.00141 0.00639 0.02912 0.057 0.00040 0.104 0.00072 0.191 0.00133 0.840 1.050 1.315 1.660 0.109 0.113 0.133 0.140 0.622 0.0518 0.824 0.0687 1.049 0.0874 1.380 0.1150 0.3869 0.679 1.100 1.904 0.2406 0.5595 1.154 2.628 0.1497 0.4610 1.210 3.625 0.09310 0.3799 1.270 5.005 0.304 0.00211 0.533 0.00371 0.864 0.00600 1.495 0.01040 1.900 2.375 2.875 3.500 0.145 0.154 0.203 0.216 1.610 0.1342 2.067 0.1722 2.469 0.2037 3.068 0.2557 2.592 4.272 6.0% 9.413 4.173 8.831 15.051 28.878 6.718 18.250 37.161 88.605 10.82 37.72 91.75 271.8 2.036 0.01414 3.355 0.02330 4.788 0.03322 7.393 0.05130 4.000 4.500 5.563 6.625 0.226 0.237 0.258 0.280 3.548 0.2957 4.026 0.3355 5.047 0.4206 6.065 0.5054 12.59 16.21 25.47 36.78 44.663 65.256 128.56 223.10 158.51 262.76 648.72 1352.8 562.2 1058. 3275. 8206. 9.886 0.06870 12.730 0.08840 20.006 0.13% 28.891 0.2006 8.625 10.75 12.75 14.0 0.322 0.365 0.406 0.438 7.981 0.6651 63.70 10.02 0.8350 100.4 11.938 0.9965 142.5 13.124 1.0937 172.24 508.36 1006.0 1701.3 2260.5 4057.7 10080. 20306. 2%66. 32380. 101000. 242470. 389340. 50.027 0.3474 78.855 0.5475 111.93 0.7773 135.28 0.9394 16.0 18.0 20.0 24.0 0.500 0.562 _ 0.593 0.687 15.000 1.250 225.0 16.876 1.4063 284.8 18.814 1.5678 354.0 22.626 1.8855 511.9 3375.0 4806.3 6659.5 11583. 50625. 81111. 125320. 262040. 759375. 1368820. 2357244. 5929784. 176.72 223.68 278.00 402.07 1.2272 1.5533 1.9305 2.7921 8.625 10.75 12.75 14.0 0.406 0.500 0.562 0.593 7.813 0.6511 61.04 9.750 0.8125 95.06 11.626 0.9688 135.16 12.814 1.0678 164.20 476.93 926.86 1571.4 2104.0 3725.9 9036.4 18268. 26%2. 29113. 88110. 212399. 345480. 47.94 74.66 106.16 128.% 0.3329 0.5185 0.7372 0.8956 16.0 18.0 20.0 24.0 0.656 0.750 0.812 0.968 14.688 1.2240 215.74 16.500 1.3750 272.25 18.376 1.5313 337.68 22.064 1.8387 486.82 3168.8 4492.1 6205.2 10741. 46544. 74120. 114028. 236994. 683618. 1222982. 2095342. 5229036. 169.44 213.83 265.21 382.35 1.1766 1.4849 1.8417 2.6552 0.405 0.540 0.675 0.095 0.119 0.126 0.215 0.0179 0.0462 0.302 0.0252 0.0912 0.423 0.0353 0.1789 0.00994 0.0275 0.0757 0.002134 0.008317 0.03200 0.000459 0.002513 0.01354 0.036 0.00025 0.072 0.00050 0.141 0.00098 0.840 1.050 1.315 1.660 0.147 0.154 0.179 0.191'' 0.546 0.0455 0.742 0.0618 0.957 0.0797 1.278 0.1065 0.2981 0.5506 0.9158 1.633 0.1628 0.4085 0.8765 2.087 0.08886 0.3032 0.8387 2.6667 0.04852 0.2249 0.8027 3.409 0.234 0.00163 0.433 0.00300 0.719 0.00499 1.283 0.00891 (continued on th next page) BDBBft ADDSfl Sfi CRANE APPENDIX 8-ENGINEERING OATA 8-17 Commercial Wrought Steel Pipe Data Schedule Wall Thickness--Per ASA B36.10-1950 Nominal Outside Pipe Diam Size eter Inches Inches 1V4 .2 2VS 3 1.900 2.375 2.875 3.5 3% 4 T5 o6 4.0 4.5 5.563 6.625 4) 8 3 10 V 12 Xa 14 8.625 10.75 12.75 14.0 16 16.0 18 18.0 20 20.0 24 24.0 8 o vH 10 12 14 V 16 X 18 c# 20 24 8.625 10.75 12.75 14.0 16.0 18.0 20.0 24.0 4 5 6 8 o 10 3 Tt3j 12 14 X c8 16 18 20 24 4.50 5.563 6.625 8.625 10.75 12.75 14.0 16.0 18.0 20.0 24.0 8 O 10 8.625 10.75 12 12.75 14 . 14.0 o 16 S 18 16.0 18.0 c# 20 20.0 24 24.0 V2 % 1 IVa iy2 2 21/2 3 0.840 1.050 1.315 1.660 1.900 2.375 2.875 3.50 4 *0 5 6 4.50 5.563 6.625 c8 8 10 12 14 8.625 10.75 12.75 14.0 16 16.0 18 18.0 20 20.0 24 24.0 Thick ness Inside Diameter dD Inches Inches Feet 0.200 0.218 0.276 0.300 0.318 0.337 0.375 0.432 0.500 0.593 0.687 0.750 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.564 11.376 12.500 0.1250 0.1616 0.1936 0.2417 0.2803 0.3188 0.4011 0.4801 0.6354 0.7970 0.9480 1.0417 0.843 0.937 1.031 1.218 14.314 16.126 17.938 21.564 1.1928 1.3438 1.4948 1.7970 0.593 0.718 0.84!) 0.937 7.439 9.314^ 11.064 12.126 0.6199 0.7762 0-. 9220 1.0105 1.031 1.156 1.281 1.531 13.938 15.688 17.438 20.938 1.1615 1.3057 1.4532 1.7448 0.438 0.500 0.562 3.674 0.302 4.563- 0.3802 5.501 0.4584 0.718 0.843 1.000 1.093 7.189 9.064 10.750 11.814 0.5991 0.7553 0.8959 0.9845 1.218 1.375 1.500 1.812 13.564 15.250 17.000 20.376 1.1303 1.2708 1.4166 1.6980 0.812 1.000 1.125 1.250 7.001 8.750 10.500 11.500 0.5834 0.7292 0.8750 0.9583 1.438 1.562 1.750 2.062 13.124 14.876 16.5 19.876 1.0937 1.23% 1.3750 1.6563 0.187 0.218 0.250 0.250 0.466 0.0388 0.614 0.0512 0.815 0.0679 1.160 ` 0.0966 0.281 0.343 0.375 0.437 1.338 1.689 2.125 2.626 0.1115 0.1407 0.1771 0.2188 0.531 3.438 0.2865 0.625 4.313 0.3594 0.718 5.189 0.4324 0.906 1.125 1.312 1.406 6.813 8.500 10.126 11.188 0.5677 0.7083 0.8438 0.9323 1.593 1.781 1.968 2.343 12.814 14.438 16.064 19.314 1.0678 1.2032 1.3387 1.6095 Inside Diameter Functions (In Inches) d1 d1 d` d 2.250 3.760 5.3% 8.410 3.375 7.290 12.536 24.389 5.062 14.136 > 29.117 70.728 7.594 27.41 67.64 205.1 11.32 14.64 23.16 33.19 38.069 56.006 111.49 191.20 128.14 214.33 536.38 1101.6 430.8 819.8 2583. 6346. 58.14 91.47 129.41 156.25 443.32 874.82 1472.2 1953.1 3380.3 8366.8. 16747. 24414. 25775. 80020. 190523. 305176. 204.89 260.05 321.77 465.01 2932.8 4193.5 5771.9 10027. 41980. 67626. 103536. 216234. 600904. 10%518. 1857248. 4662798. 55.34 86.75 122.41 147.04 411.66 807.99 1354.4 1783.0 3%2. 7526. 14985. 21621. 22781. 69357. 165791. 262173. 194.27 246.11 304.08 438.40 2707.7 3861.0 5302.6 9179.2 37740. 60572. 92467. 192195. 526020. 950250. 1612438. 4024179. 13.133 20.82 30.26 47.595 95.0% 166.47 172.49 433.5 915.7 625.1 1978. 5037. 51.6882.16 115.56 139.57 371.54 744.66 1242.3 1648.9 2671. 6750. 13355. 19480. 19202. 61179. 143563. 230137. 183.98 232.56 289.00 415.18 2495.5 3546.6 4913.0 8459.7 33849. 54086. 83521. 172375. 459133. 824804. 1419857. 3512313. 49.01 76.56 110.25 132.25 343.15 669.92 1157.6 1520.9 2402. 5862. 12155. 17490. 16819.. 51291. 127628. 201136. 172.24 . 221.30 272.25 395.06 2260.5 3292.0 4492.1 7852.1 29666. 48972. 74120. 156%9. 389340. 728502. 1222981. 3102022. 0.2172 0.3770 0.6642 1.346 0.1012 0.2315 0.5413 1.561 0.04716 0.1421 0.4412 1.811 0.02197 0.08726 0.35% 2.100 1.790 2.853 4.516 6.8% 2.395 4.818 9.5% 18.109 3.205 8.138 20.39 47.55 4.288 13.74 43.33 124.9 11.82 18.60 26.93 40.637 80.230 139.72 139.7 346.0 725.0 480.3 1492. 3762. 46.42 72.25 102.54 125.17 316.24 614.12 1038.3 1400.4 2155. 5220. 10514. 15668. 14679. 44371. 106461. 175292. 164.20 208.45 258.05 373.03 2104.0 3009.7 4145.3 7204.7 26%1. 43454. 66590. 139152. 345482. 627387. 1%9715. 2687582. - Transverse Internal Area aA Sq. In. Sq. Ft. 1.767 2.953 4.238 6.605 0.01225 0.02050 0.02942 0.04587 8.888 11.497 18.194 26. %7 0.06170 0.07986 0.1263 0.1810 45.663 71.84 101.64 122.72 0.3171 0.4989 0.7058 0.8522 160.92 204.24 252.72 365.22 1.1175 1.4183 1.7550 2.5362 43.46 68.13 %.14 115.49 0.3018 0.4732 0.6677 0.8020 152.58 193.30 238.83 344.32 1.05% 1.3423 1.6585 2.3911 10.315 0.07163 16.35 0.1136 23.77 0.1650 40.59 64.53 %.76 109.62 0.2819 0.4481 0.6303 0.7612 144.50 182.66 226.98 326.08 1.0035 1.2684 1.5762 2.2645 38.50 60.13 86.59 103.87 0.2673 0.4176 0.6013 0.7213 135.28 173.80 213.82 310.28 0.9394 1.2070 1.4849 2.1547 0.17% 0.00118 0.2%1 0.002% 0.5217 0.00362 1.057 0.00734 1.4% 2.241 3.546 5.416 0.00976 0.01556 0.02463 0.03761 9.283 0.06447 14.61 0.1015 21.15 0.1469 36.46 56.75 80.53 98.31 128.% 163.72 202.67 292.98 0.2532 0.3941 0.5592 0.6827 0.8956 1.1369 1.4074 2.0346 ,,i J&fr i -- B-18 appendix b-engineering data CRANE Commercial Wrought Steel Pipe Data (Per ASA B36.10-1950) Nominal Outside Thick Pipe Diam ness Size eter Inches Inches Inches Inside Diameter dD Inches Feet d Inside Diameter Functions (In Inches) d3 d* d Standard Wall Pipe . Vs Vs % Vt Vs 1 lVs m 2 2% 3 3% 4 5 6 O 10 12 0.405 0.540 0.675 0.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 . 4.500 5.563 -6.625 8.625 8.625 10.75 10.75 10.75 12.75 12.75 0.068 0.269 0.088 0.364 0.091 0.493 0.109 0.622 0.113 0.824 0.133 1.049 0.140 1.380 0.145 1.610 0.154 2.067 0.203 2.469 0.216 3.068 0.226 3.548 0.237 4.026 0.258 5.047 0.280 6.065 0.277 8.071 0.322 7.981 0.279 10.192 0.307 10.136 0.365 10.020 0.330 ,12.090 0.375 12.000 0.0224 0.0303 0.0724 0.1325 0.0411 0.2430 0.0518 0.3869 0.0687 0.679 0.0874 1.100 0.1150' ---- 1.904 0.1342 2.592 0.1722 4.272 0.2057 6.096 0.2557 9.413 0.2957 12.59 0.3355 16.21 0.4206 25.47 0.5054 36.78 0.6725 65.14 0.6651 63.70 0.8493. . 103.88 0.8446 102.74 0.8350 100.4 1.0075 146.17 1.000 144.0 0.0195 0.0482 0.1198 0.2406 0.5595 1.154 2.628 4.173 8.831 15.051 28.878 44.663 65.256 128.56 223.10 525.75 508.36 1058.7 1041.4 1006.0 1767.2 1728.0 0.00524 0.01756 0.05905 0.1497 0.4610 1.210 3.625 , 6.718 18.250 37.161 88.605 158.51 262.76 648.72 1352.8 4243.0 4057.7 10789. 10555. 10080. 21366. 20736. Extra Strong Pipe 0.00141 0.00639 0.02912 0.0931 0.3799 1.270 5.005 10.82 37.72 91.75 271.8 562.2 1058. 3275. 8206. 34248. 32380. 109876. 106987. 101000. 258300. 248800. Vs Vs % Vi Vs 1 lVs 1% 2 21/2 3 31/2 4 5 6 8 10 12 0.405 0.540 0.675 0.840 1.050 1.315 1.660 1.900 2.375 2.875 3.500 4.000 4.500 5.563 6.625 8.625 10.75 12.75 0.095 0.119 0.126 0.147 0.154 0.179 0.191 0.200 .0.218 0.276 0.300 0.318 0.337 0.375 0.432 0.500 0.500 0.500 0.215 0.302 0.423 0.546 0.742 0.957 1.278 1.500 1.939 2.323 2.900 3.364 3.826 4.813 5.761 7.625 9.750 11.750 0.0179 0.0252. 0.0353 0.0455 0.0618 0.0797 0.1065 0.1250 0.1616 0.1936 0.2417 0.2803 0.3188 0.4011 0.4801 0.6354 0.8125 0.9792 0.0462 0.0912 0.1789 0.2981 0.5506 0.9158 1.633 2.250 3.760 5.396 8.410 11.32 14.64 23.16 33.19 58.14 95.06 138.1 0.00994 0.0275 0.0757 0.1628 0.4085 0.8765 2.087 3.375 7.290 12.536 24.389 38.069 56.006 111.49 191.20 443.32 926.86 1622.2 0.002134 . 0.008317 0.03201 0.08886 0.3032 0.8387 2.6667 5.062 14.136 29.117 70.728 128.14 214.33 - 536.6 1101.6 3380.3 9036.4 19072. Double Extra Strong Pipe 0.000459 0.002513 0.01354 0.04852 0.2249 0.8027 3.409 7.594 27.41 67.64 205.1 430.8 819.8 2583. 6346. 25775. 88110. 223970. Vi 0.840 0.294 0.252 0.0210 0.0635 0.0160 Vs 1.050 0.308 0.434 0.0362' ~ 0.1884 0.0817 1 1.315 0.358 0.599 0.0499 0.3588 0.2149 0.004032 0.03549 0.1287 0.00102 0.01540 0.07711 lVs 1.660 0.382 0.896 0.0747 0.8028 0.7193 0.6445 0.5775 lVz 1.900 0.400 1.100 0.0917 1.210 2 2.375 0.436 1.503 0.1252 2.259 1.331 3.395 1.4641 5.1031 1.611 7.670 2'A 2.875 0.552 1.771 0.1476 3.136 3 3:500 0.600 2.300, 0.1917 5.290 5.554 12.167 9.8345 27.984 17.42 64.36 3Vi 4.000 0.636 2.728 0.2273 7.442 4 4.500 0.674 3.152 0.2627 9.935 20.302 31.315 55.383 98.704 151.1 311.1 5 5.563 0.750 4.063 0.3386 16.51 67.072 272.58 1107. 6 6.625 0.864 4.897 0.4081 23.98 117.43 575.04 2816. 8 8.625 0.875 6.875 0.5729- --47,27 324.95 2234'. 4 15360. Transverse Internal Area aA Sq. In. Sq. Ft. 0.057 0.104 0.191 0.304 0.533 0.864 1.495 2.036 3.355 4.788 7.393 9.886 12.730 20.006 28.891 51.161 50.027 81.585 80.691 78.855 114.80 113.10 0.00040 0.00072 0.00133 0.00211 0.00371 0.00600 0.01040 0.01414 0.02330 0.03322 0.05130 0.06870 0.08840 0.1390 0.2006 0.3553 0.3474 0.5666 0.5604 0.5475 0.7972 0.7854 0.036 0.072 0.141 0.234 0.433 0.719 1.283 1.767 2.953 4.238 6.605 8.888 11.497 18.194 26.067 45.663 74.662 108.434 0.00025 0.0005 0.00098 0.00163 0.00300 0.00499 0.00891 0.01225 0.02050 0.02942 0.04587 0.06170 0.07986 0.1263 0.1810 0.3171 0.5185 0.7528 0.050 0.148 0.282 0.630 0.950 1.774 2.464 4.155 5.845 7.803 12.966 18.835 37.122 0.00035 0.00103 0.00196 0.00438 0.00660 0.01232 0.01710 0.02885 0.04059 0.05419 0.09006 0.1308 0.2578 CRANE Flow OF FLUIDS THUOUO^V'AtVK, FITTINGS, AND FIPS APPENDIX C Bibliography cr R.A. Dodge & M. J. Thompson, "Fluid Mechanics"; McGraw-Hill Book Company, Inc., 1937; pages 193,288, and 407. 5H. 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Moody, "Friction Factors for Pipe Flow"; Trans actions of the American Society of Mechanical Engineers, Volume 66, November, 1944; pages 671 to 678. "A. H. Shapiro, "The Dynamics and Thermodynamics of Compressible Fluid Flow"; The Ronald Press Company, 1953, Chapter 6. "O'Brien and Hickox, "Applied Fluids Mechanics"; McGraw-Hill Book Co., Inc., New York, 1937; page 211. "K.H. Beij, "Pressure Losses for Fluid Flow in 90 Degree Pipe Bends"; Journal of Research of the National Bureau of Standards, Volume 21, July, 1938. "Walker, Lewis, McAdams, and Gilliland, "Principles of Chemical Engineering"; McGraw-Hill Book Co., Inc., New York, 1937; pages 85 and 86. . "Bingham, E.C. and Jackson, R.F., Bureau of Standards Bulletin 14; pages 58 to 86 (S.P. 298, August, 1916) (1919). !4T. R. Weymouth, Transactions of the American Society of Mechanical Engineers, Volume 34, 1912; page 197.