Document NGz6mXMLpkxaEg04aDdBJDB7D

ANSI/AWWA C403-78 (First Edition) AWWA STANDARD PRACTICE for THE SELECTION OF ASBESTOS-CEMENT TRANSMISSION AND FEEDER MAIN PIPE, SIZES 18 IN. THROUGH 42 IN. StiCAN NATIONAL) STANDAADBW 9 Approved by A WWA Board of Directors Jan. 28, 1978. Approved by American National Staixdards Institute, Inc., Jttl. 17, 1978. AMERICAN WATER WORKS ASSOCIATION 6666 West Quincy Avenue. Denver, Colorado 80235 CTD031400 Committee Personnel The Standards Committee on Asbestos-Cement Pressure Pipe that reviewed and approved this standard had the following personnel at the time of approval R. S. Bryant, Chairman J. L, Warden, Vice-Chairman T. R. Gillen, Secretary Consumer Members S. C. Baker, Naval Facilities Engineering Command, Alexandria, VA L. C. Bradley, Fort Worth W'ater Department, Forth Worth, TX R. S. Bryant, Department of Water and Power, Los Angeles, CA F. G. Denson, Works and Operations Department, Winnepeg, Manitoba R. Graff, Water Utilities, San Diego, CA J. E. Johnson,* US Bureau of Reclamation, Denver, CO R. A. Marchand, Water Department, Warren, OH J. L. Warden, US Bureau of Reclamation, Denver, CO (NAVFAC) (AWWA) (ASCE) (AWWA) i (AWWA) 'J (BUREC) 1 (AWWA) * (BUREC) General Interest Members G. C. Anderson, Insurance Services Office, New York, NY R. A. Barrows, C. E. Maguire, Inc., Waltham, MA V. R. Bickel, Department of Environmental Health, Albuquerque, NM S. L. Bishop,* Metcalf & Eddy, Boston, MA C. L. Frick,* Insurance Services Office, New York, NY R. S. Holmgren Jr., James M. Montgomery, La Jolla, CA F. A. Obert, Metcalf & Eddy, Boston, MA J. S. Slicer, Factory Mutual Research, Norwood, MA M. R. Suchomel, Underwriters Laboratories, Northbrook, IL W. Taggart, Wright-McLaughlin Engineering, Denver, CO (ISO) (NEWWA) (APWA) ' (NEWWA) (ISO) . (awwaA (WPCF)" (FMR) (UL) (ASCE) Producer Members A. E. Alpine, Cement Asbestos Products Co., Birmingham, AL T. R. Gillen, Johns-Manville Sales Corp., Denver, CO J. C. Jackson, Asbestos-Cement Pipe Producers Association, Washington, DC E. J. Lawless, CertainTeed Products Corp., Valley Forge, PA H. L. Olson,* Johns-Manville Sales Corp., Denver, CO (AWWA)! (AWWA) * Alternate Copyright 1978 by American Water Works Assn. Printed in US ii CTD031401 Table of Contents SEC. PAGE Foreword I. History of Standard............................... v II. Discussion................................................. vi Standard 1 General...................................................... 1.1 Scope.......................................................... 1 1 2 General Design...................................... 2.1 Strength and Design Factors............. 2.2 Combined Loading Theory................ 2.3 Three-Edge Bearing Load................ 2 2 2 3 3 External Loads....................................... 3.1 Introduction............................................ 3.2 Earth Loads............................................. 3.3 Superimposed Loads............................. 4 4 4 20 SEC. PAGE 4 Impact Factors....................................... 21 5 Values of Load Coefficients C, for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit.................. 21 6 Concentrated Superimposed (Wheel) Load on Asbestos-Cement Transmission Pipe--Single Wheel = 16 000 lb (H-20)............. 22 7 Design Internal Pressure and Design External Load Intercepts for Use With Selection Curves. ... 25 8 Minimum Safety Factors for Use With Asbestos-Cement Transmission-Pipe Selection.......... 25 Cl Present Worth of an Income of $1 a Year for the Next n Years............. C5,9 4 Hydrostatic Pressure........................... 4.1 Introduction............................................ 4.2 Operating Pressure ........................... 4.3 Surge Pressure........................................ 22 22 23 23 5 Pipe Selection......................................... 5.1 Combined Loading Curves................. 5.2 Safety Factors......................................... 5.3 Use of Selection Charts for Economical Design........................... 5.4 Illustrative Problem on Pipe Selection................................................ 24 24 24 24 25 Appendices A Friction Loss of Head Chart............. A1 B Surge Pressure Analysis...................... B1 B.l Water Hammer or Surge......... B1 B.2 Water Hammer Analysis......... B2 B.3 Valve Closure............................... B2 B.4 Pumped Systems......................... B4 B.5 Methods of Control................... B5 B.6 Surge Calculation Example. . . B6 B.7 Air in Pipelines............................ B7 C Frictional Power Requirements........ Cl Tables 1 Correlation of Bedding Conditions, Pipe Size, and Bedding Load Factors.................................................. 3 2 Earth Loads (lb/Iin ft)........................ 7 3 Recommended Safe Design Valuesof c for Tunnel Conditions.................. 18 Figures 1 Bedding Conditions............................... 2 Load Pressure Curve.......................... 2 3 3 Crushing Test Assembly..................... 3 4 Classification of Construction Techniques........................................... 5 5 Values of G for Trench Conditions. 6 6 Embankment Conditions.................... 12 7 Values of Cc for Positive Projecting Pipe......................................................... 8 Values of BJBi at Which the Trench and Positive Projecting Pipe Equations Give Equal Loads........ 13 14 9 Values for C,, for Negative Projecting Pipe and Imperfect Ditch Conditions............................................ 16 10 Projection Ratio (p) for the Negative Projecting Pipe Embankment Condition.............................................. 17 11 Projection Ratio (p) for the Imperfect Trench Embankment Condition.............................................. 12 Values of Ct for Tunnel Conditions. 18 19 13 Superimposed Loads............................. 20 14 Combined Loading Curves for Pipe Sizes 18 In. Through 42 In. . . . 27, 36 B1 Time {Te) = Effective for Full Cut Off Uniformly at Maximum Rate. B3 Cl Yearly Power Cost to Compensate for Friction Loss of Head................ C2,3 in CTD031402 Foreword I This foreword is for information only and is not a part of A WWA C403 I. History of Standard A new pipe material consisting of an intimate mixture of portland cement and asbestos fibers was intro duced to the North American market in 1931 following several years of usage in other countries, particularly Italy. In the ensuing years, this type of pipe gained popularity, and in 1949 AWWA established a committee on standard specifications for asbestoscement pipe under the chairmanship of S. M. Clark of Greeley and Hanson, Chicago. The committee developed a stan dard for asbestos-cement water pipe which was approved by the AWWA Board of Directors as tentative, AWWA C400-53T, May 15, 1953. In 1958, the committee was reacti vated as Committee 8340D on Asbes tos-Cement Pipe under the chairman ship of Roy H. Ritter, Whitman, Requardt and Assocs., Baltimore, to review several suggested changes and to recommend revisions to the stan dard. The committee produced a revised tentative standard adopted as AWWA C400-64T, Jan. 27, 1964. It was advanced to standard without revision Jul. 2, 1965 and designated as AWWA C400-65. The committee concluded that an installation guide was desirable to bring to the attention of users certain important requirements on the inspec tion, handling, installation, and field testing of asbestos-cement pressure pipe. The committee submitted its final draft in 1963, and it received approval as tentative, AWWA C603- 64T, Jan. 27, 1964. It was advanced to standard without revision Aug. 9, 1965 and designated as AWWA C603-65. In early 1968, the committee was reactivated as the Standards Com mittee on Asbestos-Cement Pipe to review and revise all AWWA stan dards on asbestos-cement pipe. The committee produced a revised stan dard approved by the AWWA Board of Directors Jan. 31, 1972, designated as AWWA C400-72, "Standard for Asbestos-Cement Pressure Pipe for Water and Other Liquids." AWW'A C401-64, "Standard Prac tice for the Selection of AsbestosCement Water Pipe" (originally des ignated Handbook H2), was first approved by the AWWA Board of Directors Jan. 27, 1964. Although it covered pipe sizes up to and including 36 in., it was primarily intended for use with asbestos-cement pipe in smaller distribution sizes (4 through 16 in.). In the winter of 1972-1973 the committee was reorganized and en larged to include representatives of national organizations having an in terest in the scope of the committee and wishing to participate in the work. The reorganized committee reaffirmed AWWA C400-72 without revision so that it could be presented to the American National Standards Institute for designation as an Ameri can National Standard. In 1975 the committee produced a revised standard that was approved by the AWWA Board of Directors Jan. 26, 1975, and designated AWWA CTD031403 VI FOREWORD C400-75, "Standard for AsbestosCement Pressure Pipe, 4 in. Through 24 in., for Water and Other Liquids." The asbestos-cement pipe manufac turers have developed a new series of large pipe classifications, designed to give greater freedom of selection to design engineers. This is of particular significance for large diameter pipeline projects where the savings in material cost can exceed the increased cost of more detailed design, better control of methods of installation, and pro vision of surge controls when justified. To provide the user with a ready reference and specification for this type of pipe, known as transmission pipe, the committee produced and the AWWA Board of Directors approved AWWA C402-75, "Standard for As bestos-Cement Transmission Pipe, 18 in. Through 42 in., for Water and Other Liquids." The possibility of confusion between the two 1975 standards, AWWA C400 and C402, was carefully reviewed by the committee. The results were AWW'A C402-77, which covers sizes 18 through 42 in., and AWWA C400-77, which covers sizes 4 through 16 in. There is now no overlap of sizes. Consequently, it was desirable to revise AWWA C401-64 so that it would be directly compatible with AWWA C400-77, and to develop a new pipe selection standard to be directly compatible with AWWA C402-77. AWWA C401-77 and this new standard, AWWA C403, "Stan dard Practice for the Selection of Asbestos-Cement Transmission and Feeder Main Pipe, Sizes 18 in. Through 42 in.," are the result. II. Discussion t he effect of water hammer gener ated by the opening and closing of fire hydrants can be of significant magni tude in small distribution pipe sizes, due to the high velocities generated by open hydrant flow conditions. Furthermore, it is difficult to accu rately evaluate the magnitude of these surges; and, if calculated, con trol through the use of surge tanks or other devices is impractical. Rather than employ a rule-of-thumb allow ance for surge based upon an assumed velocity change, to compensate for undetermined surge pressures AWWA C400-77 (covering sizes 4 through 16 in.) incorporates a large fixed safety factor for each asbestos-cement pres sure class. In large transmission and feeder main pipe sizes the effect of surge pres sures generated by the opening and closing of fire hydrants connected to smaller diameter distribution pipelines is of significantly lower magnitude. For example, the surge pressure gener ated by hard closure of a hydrant con nected to a 6-in. distribution line would be nine times greater than that which would occur in an 18-in. feeder main supplying a 6-in. distribution line. Major surge pressures in large transmission or feeder main pipelines, caused by stopping and starting pumps and similar components, are more readily calculated. It also is more economically practical to control these surges by incorporating into the system design a variety of devices which will reduce anticipated surge pressures to lower levels. This stan dard is based on individually evaluat ing all stress loadings placed on a pipe and on applying adequate safety fac tors, commensurate with a complete review of all design criteria. CTD031404 American Waterworks Association ANSI/AWWA C403-78 (First Edition) AWWA Standard Practice tor The Selection of Asbestos-Cement Transmission and Feeder Main Pipe, Sizes 18 in. Through 42 in. Section 1--General Sec. 1.1 Scope This standard has been prepared so that design engineers may quickly determine the correct strength classifi cation of asbestos-cement transmis sion pipe to use under various com binations of internal pressure (static, operating, and surge) and external load (earth and superimposed live loads). Combined loading curves de picting the relationship between hy drostatic loading and external loading capabilities are included to expedite the selection of the correct pipe strength classification. Note: Information to assist the engineer in selecting the most eco nomical size of pipe is in the ap pendices. Appendix A contains a friction loss of head chart based on the Hazen and Williams formula. Appendix B is a detailed analysis of surge pressure factors. Appendix C includes tables to assist the engineer in determining the yearly power costs to overcome friction loss of head. The appendices are for information only and are not part of AWWA C403. 1.1.1 Pipe classifications. The pipe strength classifications of 30, 35, 40, 45, 50, 60, 70, 80, and 90 refer to the similarly numbered classifications specified in AWWA C402, "Standard for Asbestos-Cement Transmission Pipe, 18 In. Through 42 In., for Water and Other Liquids.'' 1.1.2 Installation. Detailed cover age of the installation of asbestoscement pipe can be found in AWWA C603, "Standard for the Installation of Asbestos-Cement Pressure Pipe." CTD031405 2 A-C TRANSMISSION AND FEEDER MAIN PIPE Section 2--General Design Sec. 2.1 Strength and Design Factors The strength of asbestos-cement transmission pipe must be sufficient to withstand the combined forces of all types of internal pressures (static, operating, and surge) and external loadings (earth, live, and impact). Sound engineering practice also re quires that adequate safety factors be applied to strength requirements to ensure performance under other than ideal or calculated loading conditions. The magnitude of these safety factors is inversely proportional to the confifidence that the designer has in engineering estimates of actual operat ing conditions. Suggested safety fac tors based on experience are in cluded under specific design factor subheadings. 2.1.1 Bedding conditions. The bed ding conditions described in Fig. 1 have been selected as representative of typical installation conditions en countered in the field. Descriptions of bedding conditions are as follows: Class A--Gravel or sand base, back fill compacted. (Approximately 80% Standard Proctor, AASHTO T-99.) Class B--Same as A, but backfill not compacted. Class C--Pipe laid on earth mounds or pipe barrel on flat trench bottom with excavated coupling holes, back fill compacted. (Approximately 90% Standard Proctor, AASHTO T-9.) Class D--Pipe barrel on flat trench bottom with excavated coupling holes, backfill not compacted. Sec. 2.2 Combined Loading Theory Tests of asbestos-cement pipe under various combinations of internal pres sure and external crush load applied in three-edge bearing (see Sec. 2.3) Fig. 1. Bedding Conditions Class A bedding conditions are shown in (a) and (b). Class C conditions are shown in (c) and (d). In all four diagrams, the lightly shaded area represents approved backfill, not frozen and free from lumps, large stones, boulders, or other unsuitable substances. The heavily shaded areas represent approved backfill, carefully compacted in 4-in. layers. In (a), a minimum of 2 in. of sand is placed in a shaped bottom under the pipe. In (b), the pipe is bedded in a gravel base. In (c), the pipe barrel rests on earth mounds and then the backfill between the earth mounds is com pacted. In (d), the pipe barrel is resting on the flat bottom of the trench. Class B condition is the same as Class A, and Class D is the same as Class C except that the backfill is not compacted in B or D. indicate that there is a relationship between the combined loads at the point of pipe fracture. This relation ship can be represented by a parabolic curve as shown in Fig. 2. The equa tion for the load pressure parabolic curve, which is known as the Schlick formula, may be expressed as: in which, P is the internal pressure, in pound CTD031406 SECTION 2 3 Fig. 3. Crushing Test Assembly P represents the internal pressure; \V the external load. per square inch, that will burst the pipe when no external load exists. W is the external load, in pounds per lineal foot of pipe in the three-edge bearing test, that will crush the pipe when no internal pressure exists. pr is the internal pressure, in pounds per square inch which, in combination with some external load wt applied in three-edge bearing, will fracture the pipe. wt is the external load, in pounds per lineal foot of pipe applied in threeedge bearing which, in combination with some internal pressure pr, will fracture the pipe. The diagram at the left shows a side view of the test assembly; that at the right, an end view. P represents load; R, approximately 0.5 in.--the radius of the bearings; D, the nominal diameter of the pipe; and C, the clear space between sup ports. C should be approximately 1 in./ft of internal pipe diameter but in no case less than 1 in. it is necessary to apply a bedding load factor to the laboratory threeedge bearing loads to correlate them to the actual field loads. Since the external load equals the bedding fac tor times the three-edge bearing load, the bedding factor equals the external load divided by the three-edge bearing load. Table 1 shows bedding factors to be applied for each of the bedding conditions described in Fig. 1. TABLE 1 Sec. 2.3 Three-Edge Bearing Load Correlation of Bedding Conditions, Pipe Size, and Bedding Load Factors The combined loading curve shown in Fig. 2 is calculated on the basis of crush strengths determined by labora tory tests employing the three-edge bearing test method, which utilizes hardwood test blocks (Fig. 3). Be cause the field supporting strength of a pipe is influenced by the bedding conditions and by the lateral pressure acting against the sides of the pipe, Bedding Class A B C D Pipe Size in. 18-20 24-42 18-42 18-20 24-42 18-42 Bedding Load Factor 1.8 2.0 1.5 1.4 1.5 1.1 CTD031407 4 A-C TRANSMISSION' AND FEEDER MAIN PIPE Section 3--External Loads Sec. 3.1 Introduction For the design of asbestos-cement transmission pipe external loads (ter) are defined by the following equation : Vr = ~B~F-- t-q 2 in which, ic'r = the total external load in pounds per linear foot of pipe applied in three-edge bearing that, in com bination with some internal pressure, pr, will fracture the pipe. U'k -- the total earth load in pounds per linear foot of pipe to which the pipe is subjected. The magnitude of this load is a direct function of the burial conditions encountered or specified (trench, embankment, tun nel, etc.). u's = the total superimposed load, in pounds per linear foot of pipe, transmitted through the burial en vironment to the pipe by factors other than the earth loads. These loads can be static, dynamic, or a combination of both. B.F. = the bedding load factor, which is a load factor correlating three-edge bearing test loads to field loads associated with specific bedding conditions. (For a more explicit explanation see Sec. 2.3.) S.F. = the design safety factor specified by the design engineer. Safety factors are based on judgment, past experience, and sound engineer ing principles. For asbestos-cement transmission pipe, a design minimum safety factor of 1.5 is recommended for external loads. Sec. 3.2 Earth Loads Earth loads (wE) to which pipe is subjected are a function of the soil density, pipe diameter, depth of cover, and construction techniques employed in laying the pipeline. They depend on the interplay between the weight of the prism of earth directly over the pipe, called the interior prism, and the frictional shearing forces, plus or minus, transferred to that interior prism by the adjacent outside prisms of earth. The magnitude of earth loads varies with the construction technique employed. There are two major construction techniques nor mally encountered: trench and em bankment. Another technique, the tunnel condition, is not normally found, but nevertheless has unique design methods which make its in clusion in this discussion necessary. Fig. 4 shows these three construction techniques. 3.2.1 Marslon's equation. For as bestos-cement transmission pipe de sign, earth loads are calculated by the general form of .Marston's equation: in which, = CwcB Eq 3 U'f. = the total earth load trans mitted to the pipe in pounds per linear foot of pipe. u\ = the soil density in pounds per cubic foot. Soil densities range in value from 100 to 135 lb/cu ft. In the absence of accurate soil density information, a value of 120 lb/cu ft is recommended for asbestos-cement transmission pipe design. B = the trench width or pipe diam eter measured in feet. The value chosen depends on the installation conditions employed in laying the pipe. C -- a coefficient that is dependent upon CTD031408 SECTION 3 Classification of construction conditions for determination of loads on conduits 5 Trench* Embankment Tunnel Top natural /Top natural ground ground - Positive projecting 1 Top embankment Zero projecting 1 Top embankment Negative projecting 1 Top embankment Imperfect trench 1 Top embankment Top natural grounds Ml** Be ,H . T Top natural ground M op natural ground 'Top natural ground Stage |construction| Compacted, fill 'Top natural ground 1 Bd within required limit, otherwise conduit is positive projecting Fig. 4. Classification of Construction Techniques Reprinted by permission from WPCF Manual of Practice Ho. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. 1. Ratio of the height of fill to the width of trench or pipe diameter. 2. Shearing forces between the interior and adjacent earth prisms. 3. Direction and amount of rela tive settlement between in terior and adjacent earth prisms for embankment con ditions. The calculations used to find the value of the coefficient will depend on the installation conditions employed in laying the pipe. Values for B and C must be deter mined to calculate earth loads by Eq. 3 for the trench, embankment, and tunnel construction techniques. The following subsections describe the different conditions and explain the methods for finding the values needed to use Marston's equation for soil loading. 3.2.2 Trench condition. A trench condition is defined as that in which the pipe is installed in a narrow trench, generally less than two to three diameters in width, cut in un disturbed ground and backfilled to the original ground surface, as illus trated in Fig. 4. For this condition, Eq 3 is rewritten as: in which, we = CdWtBi2 Eq 4 Bd = the trench width in feet, measured at the top of the pipe. Cd = the load coefficient which is a function of the ratio H/Bd, where H is the height of the backfill in feet, measured to the top of the pipe, and Bd is the trench width as previously defined. 3.2.2.1 The values of Cd are ob tained from Fig. 5, in which curves A, B, C, D, and E take into account the CTD031409 6 A-C TRANSMISSION AND FEEDER MAIN PIPE m Fig. 5. Values of Ct for Trench Conditions Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. friction coefficient between the back fill and the sides of the trench for the various soil compositions likely to be encountered.' Curve A is for granular materials without cohesions. Curve B is for sand and gravel. Curve C is for saturated top soil. Curve D is for clay. Curve E is for saturated clay. Table 2 contains a series of eartn load selection tables and is included as a convenience. 3.2.3 Embankment condition. An embankment condition is defined as either that condition where the pipe is installed in a trench that is wider than two to three pipe diameters and that is cut in undisturbed ground, or that condition where the pipe is CTD031410 L SECTION 3 7 TABLE 2 Earth Loads (Ib/lineal ft) Note: Values are for clay (part D of Fig. 9, = K*i' = 0.130) with weight of earth taken as 120 Ib/cu ft. Correction for other earth weights may be made by simple direct proportions. For corrections for other types of soils, refer to formulas in Sec. 3. Boldface figures indicate maximum earth load for depth of trench. Pipe size 18 in. ID Trench Cover ft 2 2.3 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 2.5 490 640 810 1 000 1 200 1 350 1 500 1 600 1 725 1 850 2 050 2 200 2 300 2 400 2 500 2.75 640 835 1 110 1 320 1 520 1 690 1 850 2 000 2 120 2 360 2 570 2 720 2 840 3 000 3.0 1 240 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 4.0 4.5 5.0 5.5 1 640 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 2 825 3 230 3 550 4 000 4 400 4 800 5 100 5 350 3 635 4 440 5 220 5 640 6 040 6 400 6 040 6 830 7 450 7 620 Transition Width 2 ft 5 in. 2 ft 8 in. 2 ft 10 in. 3 ft 1 in. 3 ft 5 in. 3 ft 8 in. 3 ft 10 in. 4 ft 0 in. 4 ft 1 in. 4 ft 3 in. 4 ft 5 in. 4 ft 7 in, 4 ft 9 in. 5 ft 0 in. 5 ft 2 in. Pipe size 20 in. ID Trench Cover it 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width-~ft 2.75 545 705 870 1 110 1 320 1 520 1 690 1 850 2 000 2 120 2 380 2 570 2 720 2 840 3 000 3.0 890 1 250 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 1 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 3.75 4.0 4.5 5.0 5.5 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 1 770 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 2 220 2 655 3 000 3 300 3 650 4 000 4 400 4 800 5 100 5 350 3 09S 3 545 3 980 4 660 5 200 5 640 6 040 6 400 4 310 5 760 6 450 7 060 7 450 6 640 7 500 8 410 Transition Width 2 ft 8 in. 2 ft 10 in. 3 ft 0 in. 3 ft 4 in. 3 ft 8 in. 3 ft 11 in. 4 ft 1 in. 4 ft 3 in. 4 ft 5 in. 4 ft 6 in. 4 ft 10 in. 5 ft 1 in. 5 ft 2 in. 5 ft 4 in. 5 ft 7 in. CTD031411 8 A-C TRANSMISSION AND FEEDER MAIN PIPE TABLE 2--Continued Pipe size 21 in. ID Trench n 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--// 2.75 570 745 870 l no 1 320 1 520 1 690 1 850 2 000 2 120 2 360 2 570 2 720 2 340 3 000 3.0 730 915 1 250 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 1 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 1 380 l 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 3.75 1 360 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 880 4.0 2 325 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 2 795 3 250 3 725 4 140 4 660 5 200 5 540 6 040 6 400 5.0 4 210 5 160 6 000 6 450 7 050 7 450 5.5 6 100 7 020 7 950 8 460 6.0 8 920 Pipe size 24 in. ID Transition Width 2 ft 9 in. 2 ft 11 in 3 ft 2 in. 3 ft 6 in. 3 ft 10 in 4 ft 1 in. 4 ft 4 in. 4 ft 6 in. 4 ft 7 in. 4 ft 9 in. 5 ft 0 in. 5 ft 3 in. 5 ft S in. 5 ft 6 in. 5 ft 8 in. Trench friypr ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--/ 3.0 630 80S 955 1 250 1 450 1 700 1 900 2 100 2 250 2 400 2 675 2 900 3 100 3 275 3 400 3.25 810 1 010 I 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 3.5 1 010 1 400 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 3.75 1 490 1 940 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 4.0 2 030 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 2 550 3 080 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 5.0 3 620 4 130 4 660 5 400 6 000 6 450 7 050 7 450 5.5 4 660 5 740 6 750 7 410 8 000 8 460 6.0 6.5 6 800 7 850 8 910 9 600 10 000 Transition Width 3 it l in. 3 k 3 in. 3 ft 5 in. 3 ft 9 in. 4 ft 1 in. 4 ft 5 in. 4 ft 8 in. 4 ft 10 in. 5 ft 0 in. 5 it 2 in. 5 ft 5 in. 5 ft 8 in. 5 ft 1 1 in. 6 n 1 in. 6 ft 2 in. CTD031412 SECTION 3 9 TABLE 2--Continued Pipe size 27 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 3.25 3.5 3.75 4.0 4.5 5.0 5.5 6.0 6.5 7.0 710 895 1 040 1 330 1 610 1 865 2 090 2 320 2 510 2 725 3 020 3 280 3 515 3 720 3 995 90S 1 095 1 400 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 1 540 1 940 2 210 2 515 2 765 3 040 3 240 3 660 4 050 4 350 4 620 4 860 1 600 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 2 200 2 735 3 110 3 480 3 790 4 140 4 660 S 200 5 840 6 040 6 400 3 385 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 3 980 4 590 5 190 6 060 6 750 7 410 8 000 8 460 6 390 7 550 8 300 9 000 9 600 7 560 8 800 9 960 10 890 10 000 11 180 Transition WidLh 3 ft 5 in. 3 ft 6 in. 3 ft 8 in. 4 ft 1 in. 4 ft 6 in. 4 ft 8 in. 5 ft 1 in. 5 ft 3 in. 5 ft 6 in. 5 ft 7 in. 6 ft 0 in. 6 ft 3 in. 6 ft 6 in. 6 ft 8 in. 6 ft 10 in. Pipe size 30 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 3.5 755 965 1 150 1 400 1 750 2 050 2 300 2 525 2 750 2 950 3 300 3 600 3 900 4 150 4 350 4.0 1 185 1 675 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 4.5 1 680 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 Trench Width5.0 5.5 6.0 6.5 7.0 7.5 2 340 3 005 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 3 665 4 320 4 840 5 260 6 060 6 750 7 410 8 000 8 460 4 980 5 660 6 800 7 550 8 300 9 000 9 600 6 990 8 320 9 210 9 960 10 890 8 320 9 610 10 980 11 890 10 980 12 300 Transition Width 3 ft 7 in. 3 ft 10 in. 3 ft 11 in. 4 ft 5 in. 4 ft 8 in. 5 ft 0 in. 5 ft 5 in. 5 ft 7 in. 5 ft 10 in. 6 ft 1 in. 6 ft 5 in. 6 ft 9 in. 7 ft 0 in. 7 ft 3 in. 7 ft 5 in. CTD031413 10 A-C TRANSMISSION AND FEEDER MAIN PIPE TABLE 2--Continued Pipe size 33 in. ID Trench Cover St 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--/( 3.15 4.0 4.5 s.o 5.5 6.0 6.5 7.0 7.5 8.0 810 1 oso 1 220 1 540 1 940 2 210 2 SIS 2 70S 3 040 3 240 3 660 4 050 4 350 4 620 4 860 1 060 1 290 1 675 2 OSO 2 400 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 S 575 1 815 2 33S 2 800 3 no 3 480 3 790 4 140 4 660 5 200 S 640 6 040 6 400 2 445 3 OSO 3 500 3 900 4 300 4 700 S 400 6 000 6 450 7 050 7 450 3 205 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 3 925 4 640 5 400 5 000 6 800 7 550 8 300 9 000 9 600 5 610 6 070 7 450 8 350 9 210 9 960 10 890 7 550 9 030 10 110 11 060 11 890 10 470 12 120 13 020 13 390 Transition Width 3 ft 10 in. 4 ft in. 4 ft 3 in. 4 ft 6 in. 5 ft 1 in. 5 ft 5 in. 5 ft 8 in. 6 ft in. 6 ft 3 in. 6 ft 5 in. 6 ft 10 in. 7 ft 2 in. 7 ft 5 in. 7 ft 9 in. 7 ft 11 in. Pipe size 36 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--// 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 920 1 130 1 325 1 675 2 050 2 400 2 700 3 000 3 300 3 550 4 000 4 400 4 800 5 100 5 350 925 1 145 1 550 1 950 2 335 2 800 3 110 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 1 950 2 555 3 050 3 500 3 900 4 300 4 700 5 400 6 000 6 450 7 050 7 450 2 555 3 340 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 3 340 4 160 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 4 950 5 760 6 430 7 450 8 350 9 210 9 960 10 890 5 760 6 540 8 150 9 170 io no 11 060 11 890 8 150 9 750 11 000 12 150 13 020 9 750 11 330 12 900 14 140 12 900 14 510 Transition Width 4 ft 3 in. 4 ft 4 in. 4 ft 7 in. 4 ft 11 in. 5 ft 3 in. 5 ft 8 in. 6 ft 0 in. 6 ft 2 in. 6 ft 8 in. 6 ft 10 in. 7 ft 4 in. 7 ft 8 in. 7 ft 11 in. 8 ft 2 in. 8 ft 6 in. CTD031414 SECTION 3 11 TABLE 2--Continued Pipe size 39 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--// 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 990 1 290 1 520 1 950 2 335 2 800 3 no 3 480 3 790 4 140 4 660 5 200 5 640 6 040 6 400 1 580 2 220 2 555 3 050 3 500 3 900 4 300 4 700 S 400 6 000 6 450 7 050 7 450 2 340 2 980 3 340 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 3 680 4 320 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 4 500 5 360 5 760 6 430 7 450 8 350 9 210 9 960 10 890 6 430 7 170 8 150 9 170 10 110 11 060 11 890 7 440 8 980 9 750 11 000 12 150 13 021 9 310 11 090 11 980 12 900 14 140 12 830 14 330 15 260 16 130 Transition Width 4 ft 5 in. 4 ft 7 in. 4 ft 9 in. 5 ft 2 in. 5 ft 6 in. 5 ft 10 in. 6 ft 3 in. 6 ft 7 in. 6 ft 11 in. 7 ft 3 in. 7 ft 8 in. 8 ft 1 in. 8 ft 5 in. 8 ft 8 in. 8 ft 11 in. Pipe size 42 in. ID Trench Cover ft 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18 20 Trench Width--ft 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 1 060 1 390 1 700 2 220 2 555 3 050 3 500 3 900 4 300 4 700 5 400 6000 6 450 7 050 7 450 2 350 3 080 3 340 3 920 4 460 4 840 5 260 6 060 6 750 7 410 8 000 8 460 3 930 4 320 4 900 5 400 5 900 6 800 7 550 8 300 9 000 9 600 4 690 5 600 5 760 6 430 7 450 8 350 9 210 9 960 10 880 6 630 7 170 8 150 9 170 10 110 11 060 11 890 7 730 8 980 9 750 11 000 12 150 13 020 9 830 10 940 11 980 12 900 14 140 11 550 13 580 14 390 15 260 15 250 16 430 16 830 Transition Width 4 ft 8 in. 4 ft 10 in. 5 fL 0 in. 5 ft 4 in. 5 ft 8 in. 6 ft 1 in. 6 ft 5 in. 6 ft 10 in. 7 ft 2 in. 7 ft 6 in. 8 ft 0 in. 8 ft 5 in. 8 ft 10 in. 9 ft 1 in. 9 ft 4 in. CTD031415 12 A-C TRANSMISSION AND FEEDER MAIN PIPE edcba ab c de Fig. 6. Embankment Conditions aa and bb The trench width is less than the transition width; earth loads are computed by the trench equation (Eq 4). cc The trench width is the transition width; earth loads arc computed by either Eq 4 or Eq 5. dd and ec The trench width is greater than the transition width; earth loads are computed by the positive projecting pipe embankment equation (Eq. 5). For a given depth of cover the earth loads resulting from trench widths cc, dd, and ee are equal. covered with fill above the original ground surface. Embankment con ditions are further subdivided into positive and negative projecting pipe categories, depending on the location of the top of the pipe relative to the original undisturbed ground. A special case where compressible ma terial is used as part of the backfill, called an imperfect trench, also is classified as an embankment con dition. The various embankment conditions are illustrated in Fig. 6. 3.2.4 Positive projecting pipe em bankment condition. A positive pro jecting pipe condition is defined as either that condition where the pipe is installed in a trench cut in un disturbed ground that is wider than two to three pipe diameters, or that condition where the top of the pipe is above the adjacent original ground surface and covered with fill above the original ground surface. For this condition, Eq 3 is rewritten as: we = CcW'Bc1 Eq 5 in which, Bc = the pipe outside diameter in feet. Cc -- the load coefficient, which is a function of the ratio H/Bc, the projection ratio p, and the settlement ratio rsd. 3.2.4.1 The values of Cc are ob tained from Fig. 7. Cc also may be obtained from Eq 6 when the follow ing conditions exist simultaneously: 1. The ratio H/Bc is greater than 1.3. 2. The product p{rt<j) = 0.7. Cc = \.W1H/BC - 0.96 Eq 6 3.2.4.2 The projection ratio p is defined as the ratio of the distance that the top of the pipe projects above the original ground surface to the pipe outside diameter. The recommended value for the settlement ratio rtd is + 0.7 for asbestos-cement transmis sion pipe design. 3.2.5 Transition width. It will be noted from the preceding discussion that under construction conditions where a trench is cut in undisturbed ground two methods of computing the earth load are available: (1) the trench condition, and (2) the positive projecting pipe embankment con dition. The method chosen is de CTD031416 SECTION 3 13 Fig. 7. Values of Ce fr Positive Projecting Pipe Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. pendent on the ratio of the trench width to the pipe diameter. As pre viously stated, when the trench width is less than two to three times the pipe diameter, earth loads are computed by the trench condition equation (Eq 4). The width of trench at which both methods of computation give equal loads is called the transition width. The earth load computed at the transition width is theoretically the maximum external earth load that can be transmitted to the pipe for any given depth of cover. For all trench widths greater than the transition width, earth loads are computed by the positive projecting pipe embank ment condition equation (Eq 5). In this latter case and for a given depth of cover, the earth loads are equal to the load that results at the transition width and that is computed by the trench condition equation (Eq 4). [See Fig. 6.] 3.2.5.1 The transition width is determined from Fig. 8 by multiplying CTD031417 0 130 = 0 1924 k ) j' = 0.130 Shaded section to enlarged scale CTD031418 Fig. 8. Values of B J B ,, at Which the Trench and Positive Projecting Pipe Equations Give Equal Loads "R tprinted by permission from WPCF Manual of Practice No. 9, Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE. 1966. SECTION 3 15 the applicable ratio Bd/Bc by the applicable pipe outside diameter (Bc). The applicable ratio of trench width to pipe outside diameter (Bd/Bc) can be obtained from Fig. 8 for any given ratio of backfill height to pipe outside diameter (H/Bc). 3.2.6 Negative projecting pipe em bankment condition. A negative pro jecting pipe condition is defined as that condition where the pipe is installed in a relatively shallow trench wherein the top of the pipe is at some elevation below the original ground surface. The trench is then backfilled and compacted, and embankment is constructed thereon to finished grade (Fig. 4). For this condition, Eq 3 is rewritten as we = CnWcBd1 Eq 7 in which, Bd = the trench width in feet, mea sured at the top of the pipe. Cn = the load coefficient which is a function of the ratio H/Bd, the pro jection ratio p, and the settlement ratio r,d- negative projecting pipes. However, as the trench width increases and the ratio Bd/Bc becomes greater than that given in Fig. 8, the earth load should be determined from Eq 5 for positive projecting pipes. Adherence to the preceding rule will result in the most realistic earth loads for design purposes. 3.2.7 Imperfect trench embankment condition. The imperfect trench em bankment condition occurs rather in frequently and is included for general information. The imperfect trench embankment condition refers to that construction technique wherein the pipe is first installed as a positive projecting pipe. A portion of the embankment is then built up to some elevation above the pipe top and thoroughly compacted as it is placed. A trench the same wfidth as the pipe is then excavated directly over the pipe down to or near to its top and subsequently backfilled with loose compressible material. The remainder of the embankment is then built up to final elevation (Fig. 11). For this condition, Eq 3 is rewritten as 3.2.6.1 The various values of Cn are obtained from Fig. 9. The pro jection ratio p is defined as the ratio of the vertical distance from the original ground surface down to the pipe top to the trench width, Bd. (See Fig. 10.) For asbestos-cement transmission pipe design the recom mended value for the settlement ratio r,d is zero. 3.2.6.2 When calculating earth loads under negative projecting pipe embankment conditions, considera tion must be given to the transition width as defined in paragraph 3.2.5. For values of the ratio Bd/Bc less than those given in Fig. 8, the load on a pipe is determined from Eq 7 for we = CnW'B? Eq 8 in which, Bc = the pipe outside diameter in feet. C,, = the load coefficient which is a function of the ratio H/Bc, the pro jection ratio p, and the settlement ratio rtd. 3.2.7.1 The various values of C,, are obtained from Fig. 9. The pro jection ratio p is defined as the ratio of the vertical distance from the top of the excavated trench down to the pipe top to the pipe diameter (Fig. 11). For asbestos-cement transmis sion pipe design the recommended CTD031419 16 i A-C TRANSMISSION AND FEEDER MAIN PIPE Fig. 9. Values of C,, for Negative Projecting Pipe and Imperfect Ditch Conditions Reprinted by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. value for the settlement ratio r,d is equal to --0.3. 3.2.8 Tunnel conditions. There are two types of tunnel construction en countered in normal pipe laying operation. 3.2.8.1. The first type is the most frequently encountered and occurs when a sleeve of a larger diameter than the specified pipe is first jacked through an embankment. The pipe is then placed into the sleeve without CTD031420 SECTION 3 Top of embankment Um Projection ratio = 17 Top of natural ground Fig. 10. Projection Ratio p for the Negative Projecting Pipe Embankment Condition becoming an integral part of the tunnel construction. In this example the sleeve supports the entire earth load and the pipe contained therein is not subjected to crushing loads. When selecting the required pipe classification for this condition, only the internal pressure needs to be con sidered for design. 3.2.8.2. The second type of tunnel condition is rarely encountered in transmission work but is discussed here for completeness. 11 occurs when .the pipe itself must carry the entire load. The area through which the pipeline must pass is bored and braced with the necessary supports. The pipe then is placed in the tunnel and the void between the pipe and tunnel braces is backfilled with compacted earth, grout, or concrete. Once this operation is completed, the earth load automatically transfers from the tun nel supports to the pipe itself. For this condition, Eq 3 is rewritten as Wg = in which, ~ 2c) Eq 9 Bt = the maximum width of the tunnel excavation in feet. c = the coefficient of cohesion in pounds per square foot. Ct = the load coefficient which is a function of the coefficient of internal fraction for the material of the tunnel and of the ratio H/Bt, where H is the distance from the ground surface to the top of the tunnel in feet and BT equals the width of the tunnel ex cavation in feet. CTD031421 18 A-C TRANSMISSION AND FEEDER MAIN PIPE Top of embankment / Projection ratio = ~ Bc Compressible backfill Top of stage construction compacted fill / Trench dug in compacted fill Natural ground / $% Fig. 11. Projection Ratio p for the Imperfect Trench Embankment Condition 3.2.8.3 Values of Cr for different types of soil are obtained from Fig. 12. If the value for the coefficient of cohesion is not available from labora tory tests, then the recommended safe design values in Table 3 are to be used. TABLE 3 Recommended Safe Design Values of c for Tunnel Conditions Material Clay, very soft Clay, medium Clay, hard Sand, loose dry Sand, silty Sand, dense Top soil, saturated Values of c 40 250 1000 0 100 300 100 3.2.8.4 When, in tunnel construc tion, the excavation becomes exces sive, or when the void surrounding the pipe or tunnel lining is not carefully filled, or when the cohesion of the undisturbed material above the tunnel construction is destroyed by soil saturation or vibration, the earth load should be calculated by Eq 4 for trench conditions. Since it can be exceedingly difficult to either predict or assess whether the tunnel excava tion is excessive, it is recommended that Eq 4 be used for most in stallations for safe asbestos-cement transmission pipe design. 3.2.8.5 It should be noted that the preceding discussion is based on the premise that the tunnel would be constructed in homogenenous soils that do not create unusual pressures and stresses. If the tunnel is con structed through materials that tend to squeeze or swell, such as some types of clay or shale, or through blocky and seamy rock, then methods other than tunnel construction must CTD031422 SECTION 3 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 19 Fig. 12. Values of Cr for Tunnel Conditions by permission from WPCF Manual of Practice No. 9, "Design and Construction of Sanitary and Storm Sewers," WPCF and ASCE, 1966. CTD031423 20 A-C TRANSMISSION AND FEEDER MAIN PIPE Concentrated superimposed toad, Wsi, vertically centered over pipe. Distributed superimposed load, Wsvertically centered over pipe. Fig. 13. Superimposed Loads be utilized. The method of instal lation that is used is the responsibility of the engineer who is in charge of construction. Sec. 3.3 Superimposed Loads Superimposed loads ws are ex ternal loads other than the normal earth loads transmitted to the pipe. There are two types of superimposed loads as illustrated in Fig. 13: (1) concentrated wsi, and (2) distributed Ws2 Superimposed loads are fre quently referred to as live loads. 3.3.1 Concentrated loads. A con centrated load is a load caused by a single force which may be either static or dynamic in nature. In normal pipe design, vehicular wheel loads are the most frequently encountered con centrated loads. The magnitude of the load produced by concentrated superimposed forces is determined by CPF viai = --7-- Eq 10 in which Wsi = the load on a pipe caused by a concentrated superimposed force in pounds per linear foot of pipe. (For convenience, concentrated superim posed loads resulting from a 16,000-lb wheel force are presented in Table 6.) P, = the concentrated force in pounds. The American Association of State Highway and Transportation Officials (AASHTO) design manual gives loads for various sizes and types of vehicles. F = the impact factor. American Association of State Highway and Transportation Officials (AASHTO) vehicular wheel loads are shown in Table 4. Impact factors vary from one locale to another and values that are consistent with local, state, and federal specifications should be chosen. L = the effective pipe length in feet. For pipe less than three feet, the actual length of the section should be used. For all other pipe lengths an effective length of three feet should be used. CTD031424 SECTION 3 21 TABLE 4 Impact Factors Depth of Cover n 1.0-2.0 2.0--3.0 3.0 or greater Impact Factor F 1.2 1.1 1.0 C, = the load coefficient, which is a function of the depth of cover to the top of the pipe and the nominal inside diameter of the pipe. Values of C, are obtained from Table 5. 3.3.2 Distributed load. A distri buted load is a load caused by a uniform force distributed equally over a given area. The load may be either static or dynamic in nature. The magnitude of the load produced by distributed forces is determined by in which, ivsi = C,P,F Bc Eq 11 wS2 = the load on a pipe caused by distributed superimposed force in pounds per linear foot of pipe. P, = the intensity of the distri buted force in pounds per square foot. F = the impact factor as explained in paragraph 3.3.1. Bc = the pipe diameter in feet. C, = the load coefficient, which is a function of the depth of cover to the top of the pipe and the nominal inside diameter of the pipe. Values of C, are obtained from Table 5. 3.3.3. Illustrative problem. An 18in. asbestos-cement transmission pipe is to be installed in a 3-ft wide trench under 8 ft of cover. The backfill is ordinary clay with a weight of 120 lb/cu ft. Determine the earth load on the pipe. Solution : The load must be com puted two ways using the Marston equations for the trench condition and for the projecting pipe condition. a. Trench condition Eq 4: w.'g = CiW'(Bd)2 H8 -- = - = 2.7 (approximately 3) Bd 3 Ci = 1.9 ^from Fig. 5 and we = (1.9)(120)(3)2 = 2100 lb/ft TABLE 5 Values of Load Coefficients C,, for Concentrated and Distributed Superimposed Loads Centered Vertically Over Conduit Pipe Bize, ID--in. 18 20 21 24 27 30 33 36 39 42 Depth of Cover ft 2 2} 3 4 5 6 8 0.391 0.422 0.436 0.478 0.510 0.543 0.563 0.590 0.615 0.619 0.289 0.316 0.327 0.362 0.392 0.423 0.446 0.470 0.502 0.516 0.221 0.241 0.251 0.280 0.306 0.332 0.353 0.375 0.404 0.422 0.136 0.150 0.157 0.177 0.195 0.213 0.230 0.248 0.272 0.286 0.092 0.102 0.107 0.120 0.133 0.147 0.159 0.171 0.191 0.202 0.066 0.073 0.077 0.087 0.096 0.106 0.115 0.124 0.140 0.147 0.038 0.042 0.044 0.050 0.056 0.062 0.067 0.073 0.083 0.089 10 0.025 0.027 0.029 0.033 0.037 0.041 0.045 0.049 0.054 0.063 12 16 0.017 0.019 0.020 0.022 0.025 0.029 0.032 0.035 0.041' 0.043 0.010 0.011 0.012 0.013 0.014 0.016 0.018 0.020 0.026 0.030 20 0.006 0.007 0.007 0.008 0.008 0.010 0.011 0.012 0.015 0.017 NJFor convenience, concentrated superimposed loads resulting from a 16OOO-lb wheel force are presented in Table o. CTD031425 22 A-C TRANSMISSION AND FEEDER MAIN PIPE TABLE 6 W81 Concentrated Superimposed (Wheel) Load on Asbestos-Cement Transmission Pipe Single Wheel = 16,000 lb (11-20 Wheel Load) Cover Over Top of Pipe ft 18 20 2 2083* 2251 2* 1541 1682 8 1178 1286 4 725 800 5 490 544 6 352 389 8 203 224 10 133 144 12 91 100 16 53 59 20 32 37 21 2364 1728 1334 837 570 410 234 154 105 64 40 24 2545 1939 1494 944 640 464 267 176 117 69 43 Pipe Diameter in. 27 2720 2091 1632 1040 710 512 299 197 133 75 45 30 2896 2256 1723 1136 784 566 330 219 155 85 53 33 2992 2368 1878 1224 845 611 357 240 170 96 60 36 3149 2510 2000 1321 912 662 390 261 187 107 63 39 3280 2677 2154 1450 1018 747 443 288 219 139 80 42 3301 2752 2250 1525 1077 784 475 336 229 160 91 * Values shown are in pounds per linear foot of pipe. Note: Table is based on impact factor of one. If different impact is to be used, simply multiply value from table times desired impact factor. b. Projecting pipe condition Eq 5: tt'E = CeU'r(Bc)2 Bc = 18 in. pipe OD = 1.7 ft Cc = 1,892 (H/Bc) - 0.96 = 1.892(8/1.7) - 0.96 = 8 we = (8) (120) (1.7)- = 2800 Ib/ft c. The engineer, knowing the job conditions and degree of inspec tion, should decide which load applies. Section 4--Hydrostatic Pressure Sec. 4.1 Introduction For the design of asbestos-cement transmission pipe, the internal hydro static pressure pT is defined by Pt -- (Po + PAS. F. in which, Eq 12 pr = the total internal pressure in pounds per square inch which, in combination with some external load wT applied in three-edge bearing, will fracture the pipe. P0 = the static or operating pres sure in pounds per square inch de fined by the design criteria. P, = the surge pressure in pounds per square inch resulting from either water hammer or other incremental pressures over and above the normal operating pressure. S.F. = the design safety factor specified by the purchaser. Safety factors are based on judgment, past experiences, and sound engineering principles. For asbestos-cement trans- CTD031426 SECTION 4 23 mission pipe design, a minimum safety factor of 2.0 is recommended. For simplicity in design and selec tion of asbestos-cement transmission pipe, the internal pressure may be separated into two components: (1) operating pressure, and (2) water hammer or surge pressure. Each will be determined separately. Sec. 4.2 Operating Pressure The operating pressure Pa is that pressure which exists under normal or steady conditions of operation. The pressure may be induced by pumps, gravity (such as the head created by a reservoir or elevated w;ater tank), or a combination of both pumps and gravity. Under a 100 percent gravity situation, the pressure in the line at a given point is somewhat higher when there is no flow and conditions are static. Under static conditions the pressure at a given point, measured in feet of head, is equal to the difference between the elevation of that point and the water surface level at the reservoir. Under flowing conditions the pressure at a given point is re duced by the amount of friction and other energy losses resulting from the flow of water from the reservoir to that point. The magnitude of this head loss may be found by using the Hazen and Williams chart in Ap pendix A. In piping systems that have long runs with relatively few fittings and accessories, the recom mended value of C (coefficient of flow) is 140. Sec. 4.3 Surge Pressure Surge pressures P, are of a transient nature and are caused by unsteady or changing conditions in the pipeline. The terms ``water hammer," "surge," or "transient pressure" are often used interchangeably to refer to these pres sures, which are of brief duration but often of considerable magnitude. A variety of conditions may cause surge pressures. These include a valve opening or closing, sudden movement of air in a line, or a pump starting or stopping. Transient pressures are often a controlling factor in the selection of pipe strength. For this reason, a pipe system should always be analyzed for surge pressure deter minations and the results should be used in pipe selection. 4.3.1. Surge control. There are numerous methods for control of surge pressures in the line. Con sideration should be given to use of these methods to limit pressures to an acceptable level. Economics plays a major role in this area. Various designs may have to be balanced, depending on the complexity of the system, to yield an economical and efficient design. 4.3.1.1 Appendix B presents a dis cussion of water hammer with em phasis on how it may be analyzed and controlled. Although the subject is discussed in some detail, and an illustrative problem is included that involves controlling surge pressure by timing a valve closure, the subject is too complex to be thoroughly covered in this standard. It is suggested that control of surge for any transmission system be discussed wfith surge control equipment manufacturers or con sultants in this particular field. The effects of surge in a pipeline, however, should not be ignored, as neglect of this factor may result in severe dam age to the system. Also, because of the number of variables involved in creating water hammer pressures, and because of the ability to regulate their magnitude with proper controls, it is ) CTD031427 24 A-C TRANSMISSION AND FEEDER MAIN PIPE not recommended that fixed water hammer allowances based on assumed velocity changes or some other single criterion be used for the larger diam <eter transmission and feeder main lines. Section 5--Pipe Selection Sec. 5.1 Combined Loading Curves Charts for Economical Design, the method for pipe selection is outlined. As discussed previously, it has been demonstrated satisfactorily by tests that asbestos-cement transmis Sec. 5.2 Safety Factors sion pipe conforms generally to the Safety factors are normally applied Schlick formula for combined loading by the engineer to his computed de (Sec. 2.2). Numerous tests have sign values of crush- and internal established values for P, internal hy pressure that are to be resisted by the drostatic design pressure with no pipe in service. These factors protect crush load applied, and for IF, ex against unforeseen loads that may be ternal crush design load with no placed on the line at some time in the internal pressure applied, for all diam future, and against other contin eters and strength classifications. gencies such as improper construction. These values represent the end points It is the engineer's prerogati\e to on the combined loading curves; the intermediate points on the curves are computed by use of the Schlick formula. (It should he noted that all values used for P and W represent a conservative interpretation of the select which safety factors he feels should apply to a given system. Con siderable field experience as well as extensive laboratory work has yielded a wealth of information on the be havior of asbestos-cement transmis . test data.) On the curves, each sion pipe. For this reason, suggestions intermediate point--wr, pr--repre for minimum safety factors are made 1 sents a combination of crush loading and internal pressure that the pipe will withstand when the loads are in Table 8. Note that, since the com bined loading principle is applicable, the safety factors will be applied to applied simultaneously. 5.1.1 Selection curves. Selection curves in Fig. 14a-- 14j are presented for each size of pipe from 18 through 42 in. On the graph for each pipe both hydro and crush simultaneously. Note also that water hammer and live load, which are both transient load conditions, are considered as acting simultaneously lor design purposes J diameter, a combined loading curve is here. Since the likelihood of both drawn for each strength classification occurring at the same time is minimal, of that pipe size. The vertical axis an additional conservative element is represents the internal hydrostatic introduced into the design. I design pressure P, and the horizontal axis represents the external three-edge bearing crush design load IF. Table 7 lists the values of P and, W for the Sec. 5.3 Use of Selection Charts for Economical Design strength classifications of each pipe After all loads on the pipe have been size. In Sec. 5.3, Use of Selection computed (operating pressure, water CTD031428 SECTION 5 25 TABLE 7 Design Internal Pressure* and Design External Load\ Intercepts for Use With Selection Curves for the Following Pipe Classifications 30 35 40 45 50 60 70 80 90 Pipe ' Size P* - 300 P = 350 in. P -- 400 P 450 P = 500 P = 600 P * 700 P = 800 P -- 900 m W W H' W W IV 14' IV 18 2 500 3 000 4 000 5 000 6 500 8 500 n ooo 14 000 18 000 20 2 500 3 500 4 500 5 500 7 100 9 500 12 ooo 1 5 000 20 000 21 2 500 3 500 4 500 5 800 7 300 9 700 12 500 16 000 21 000 24 2 800 3 800 5 000 6 200 8 100 11 000 15 000 19 000 24 000 27 3 500 4 200 5 500 7 000 8 800 12 500 16 500 20 500 27 000 30 3 500 4 500 6 000 7 500 9 700 13 500 18 000 22 500 30 000 33 3 500 5 000 6 500 8 000 10 500 14 500 19 500 24 500 33 000 36 4 000 5 000 7 000 9 000 11 200 16 000 21 000 26 000 36 000 39 4 200 5 300 7 500 9 700 12 000 17 200 22 500 28 000 39 000 42 4 300 5 700 8 000 10 500 13 000 18 500 24 000 30 000 42 000 * P-tsi. t W--IbiUn hammer, earth load, and live load), the most economical strength of pipe to meet the service conditions should be selected. The applicable selection procedure using the suggested safety factors is: 1. Add operating pressure and water hammer, Pa + P, (Sec. 4). 2. Add earth load and live load, wB + ws (Sec. 3). 3. Enter the combined loadinggraph for the appropriate pipe diam eter. Plot the values from Steps 1 and 2 above as one point. When using the left-hand scales, be sure to multiply the operating pressure plus water hammer by the suggested safety factor of 2.0. When using the bottom scale, be sure to multiply the earth load plus live load by the suggested safety factor of 1.5, and then to divide it by the bedding factor (Sec. 2.3). 4. The point plotted will lie be tween the curves for two pipe TABLE 8 Minimum Safety Factors for Use With Asbestos-Cement Transmission Pipe Selection Type of Load Safety Factor Hydro Crush Operating pressure plus water hammer, combined with earth load plus live load 2.0 1.5 strengths. Select the higher strength of the two. This repre sents the most economical selec tion consistent with engineering requirements. Sec. 5.4 Illustrative Problem on Pipe Selection A 24-in. asbestos-cement transmis sion line is to be installed in a 4-ft wide trench with 5 ft of cover. The operating pressure will be 100 psi. Surge pressures will be limited to a CTD031429 JBSB&Siai---- 26 A-C TRANSMISSION AND FEEDER MAIN PIPE maximum of 50 psi. A 16,000-lb wheel load is to be assumed, with an impact factor = 1. Class C bedding will be used. Select the proper strength of pipe to be used with safety factors of 2.0 in hydro (P0 + Ps) and 1.5 in crush (wE -p Solution : Following instructions for use of selection charts witli safety factors as described in Sec. 5.3 gives 1. P0 + P. = 100 + 50 = 150 psi 2. we + ws = 2030 + 640 = 2670 lb/ft (P,, + P,)(S.F) = 150 X 2.0 = 300 psi (we + tc.s)(5.C.) = (2670) (1.5) 4. 1.5 = 2670 lb ft 5. Consult the combined loading chart for 24-in. pipe, using the left hand and bottom scales. Plot the two loads as a single point on the chart. The point falls between T-40 and T-45. Cse T-45. \ I I I CTD031430 SECTION 5 27 Internal hydrostatic design pressure --P j psi - (Operating pressure 4 water hammer safety factor 0 2000 4000 6000 8000 10.000 12.000 14 000 External crush load -3-edge bearing --IV Ib-'ft Safety factor Wi = earth load live load -----------------------Bedding factor Fig. 14a. Combined Loading Curves for 18-in. Transmission Pipe 16.000 I CTD031431 Internal hydrostatic design pressure--P j ip s ii = ^operating pressure + water hammer safety factor I f CTD031432 SECTION' 5 29 Internal hydrostatic design pressure--P j <psn - 'O perating pressure v water ham m er' safety fa cto r 0 2000 4000 6000 8000 10.000 12.000 14,000 16.000 External crush load 3-edge bearing -- WMb/ft Safety factor Wj = `earth load - live load Bedding factor Fig. 14c. 21-in. Transmission Pipe CTD031433 Internal hydrostatic design pressure --P r psi - operating pressure ' water harmne CTD031434 SECTION' 5 31 Internal hydrostatic design pressure--P j psi - operating pressure t water hammer safety (actor External crush load 3-edge bearing --W lb. It Safety factor Wj dearth load + live load-----------------------Bedding factor Fig. 14e. 27-in. Transmission Pipe CTD031435 1000 A-C TRANSMISSION' AND FEEDER MAIN PIPE 30-in. Transmission Pipe 900 800 90 700 a) 600 .70 500 V 60 400 ___________ A 300 \ \4 ) \ 200 \ 35 \ 30 \ 100 0 2000 4000 6000 8000 10,000 12,000 14,000 16.000 External crush load i3-edge bearing -- WtIb/ft Safety factor Wr = i earth load + live load Bedding factor Pig. 14f. 30-in. Transmission Pipe SECTION 5 33 Internal hydrostatic design pressure --P j psi operating pressure r water ham m er' safety factor 0 2000 4000 6000 8000 10,000 12,000 14 000 16.000 External crush load i3-edge bearing --W- Ib/ft Safety factor WT = -earth load -r live load Bedding factor Tig. 14g. 33-in. Transmission Pipe CTD031437 Internal hydrostatic design pressure --P f 'p si- operating pressure t water ham m er, safety factor External crush load '3-edge bearing -- W Ib/ft Safety factor Wr = earth load * live load -----------------------Bedding factor Fig. 14h. 36-in. Transmission Pipe CTD031438 SECTION' 5 35 Internal hydrostatic design pressure --P f .psn - operating pressure * water ham m er' safety factor 0 4000 8000 12.000 16.000 20 000 24 000 External crush load '3-edge bearing -- W Ib/ft Safety factor Wf = .earth load t live load Bedding factor Fig. 141 39-in. Transmission Pipe CTD031439 Internal hydrostatic design pressure--Py ipsn ; (operating pressure + water ham m er' safety factor CTD031440 iSnSBaanii Appendix A Friction Loss of Head Chart--Coefficient of Flow, C = 140 This appendix is for information only and is not a part of A \Y\YA C403 OOOQ rCI-I OyI-INtI-rI OrI-I O<JIIi OCIOO<I0 ooooooo oooo5o o C~O~ DCO O CTMf DU*> (r-HiOn CM CO o2 o2( v ia Z. E^ a> n>s.~9c I tt 2- o~ ? ch E03 j<O=5 * ' a s. - . c. UJ -- ; c ^1o .oS*o" .. OS u o 5H- * Z i: oO oSCO OOO_ _ CTIOI- <C*"IMI VTII-- OYII- O5II) OoIoI OII OOOOOOO ooooooo CM cm R e p rin te d by perm ission of the J o h n a -M a n v llle Sales C o rp o ra tio n . </) </) s --C o <a o 9 in O ?5 " oi fofl u O^ O -r Job C >V IIISeo oo ^oHc8o --t= J3 x t E 8 2| -fS o" x>-_^fioX>>>JgC-o?) o Z T3 S O O iE = o 'jajsweiQ sdid A1 i o CTD031441 A2 ooo OM'-OOOO l II II II II(7) I ICO CD ooooooo oooo ooo n (5 o oj tn r-- 10 8 CD O ry CO CD CD O T- t~ CJ CO v3 O am .gE5 2 *8 . II ~ >-.9- 1-o _ -Q 2= S ! O c J? o<> o I -- i CT -- 03 k- o E E 0X3 O <rt ? Q Ui : !E2 "a, a? Spc o -c .5 OhT3 c So --o C < 03 - *. oo *o- ;5 0000 hcmt-oqoo Ir- 1-II II rI-I OII) CIDI I<D OOOOOOO OOOOOOO ifiTis co <o r? cj t- CO CD CO CN CO CD i-' C\ Osi 'f </> </> >! --o CS3 a>: 18- Z. ; * u 03 O ->O. wo* e e ' J ^ 1 E ffl >* 03 03 x: h- o 0. x/' 'jaisujBiQ adid CTD031442 Appendix B Surge Pressure Analysis This appendix 15 for information only and is not a part of A M'U'/l C403, j B.l Water Hammer or Surge The slowing down or stopping of any moving mass requires a force or forces to counterbalance the kineticenergy that keeps the mass in motion. The faster a mass is decelerated and brought to a halt, the greater the force that is required. B.l.I Forces involved. It is some what of an oversimplification, but water hammer, or surge, can be de fined in these terms: The shutting of a valve or the stopping of a pump causes a moving column of water in a pipeline to slow down and stop. The forces that bring about this deceleration are exerted radially on the moving water column by the pipeline walls. Conversely, the water exerts added pressure on the pipe, and the hoop stresses in the pipe walls jjthus increase over the normal operat' ing pressure values. The faster the column of water is brought to a halt, the higher these stresses rise. B.l.2 Rate oj velocity fluctuation. The pipe wall stresses are thus de veloped by, and increase in direct . proportion to, the internal pressure that builds up as the column of water decelerates. The slower the de celeration, the less the pressure builds up, and the less the pipe wall stresses increase. It is, therefore, of impor tance to the pipe designer to know how to control the rate of velocity fluctu ation, since by controlling this rate he controls the magnitude of the pressure variations during the transi tional periods. By such control he can keep the pipe wall stresses during surge to a predetermined value that will allow an economical installation. B. 1.3 H ave motion. W ater, being liquid, will act in a fairly complex manner when undegoing acceleration or deceleration. Pressure waves are set up which move along the pipeline at a rate of 2500--4500 ft/sec, the rate depending on the pipe wall material. The waves will continue until they encounter a boundary con dition, such as a reservoir, a closed valve, or a change in pipe diameter, at which point they will reflect hack in the opposite direction. The wave motion will oscillate back and forth in the pipe until it is dampened out bv the friction effects of the pipe walls. B.l.4 Clauses. The two major causes of water hammer or surge are 1. The closing or opening, fully or partially, of a valve in a pipeline system. The valve may be in the line for one of a number of purposes. It could be a gate valve, float valve, pressure reducing valve, or serve some other function. 2. The starting up or shutting dow n of a pump (switch or power failure) It can be seen that both of these occurrences cause changes in the velocity, and consequently in the quantity, of water flowing in the pipeline. B.l.5. Effects. Ignoring the effects of surge in the pipeline can lead to difficulties after the line is in opera- B1 B2 APPENDIX B tion. Surge can result in damaged equipment and seriously reduced capacity. B.2 Water Hammer Analysis The elastic wave theory for surge analysis has been empirically estab lished to be correct by many ex periments, the first of which were performed as early as 1890. Its application to pipeline problems will yield results which are accurate and which may be relied upon for adequate analysis. B.2.1 Wave velocity. Water ham mer pressures are a function of the maximum rate of change of how. When a valve is closed or a pump stops, a pressure ware is propagated along a pipeline. The velocity of the wave is the same as the velocity of sound in water, modified by physi cal characteristics of the pipeline; it is given by the following equation : in which, 4660 \I + kd/Ee Eq B) a = pressure wave velocity, in feet per second k = modulus of compression of water, 300,000 psi d = internal diameter of pipe, in inches = modulus of elasticity of as bestos-cement pipe, 3.400,000 psi e = wall thickness, in inches 4660 = velocity of sound in water in feet per second B. 2. 2. Maximum pressure. If the pressure wave is reflected back from a boundary condition, such as a reservoir, and returns to its initial position after the flow in the line is completely stopped, then maximum water hammer pressure for those conditions will result. Stopping of the flow may be effected by closing a valve or by a pump stoppage. The magnitude of that maximum pressure is given by Eq B2 in which, h = surge pressure, in feet of water V = velocity of water in the pipe line during normal conditions, in feet per second a = velocity of pressure wave, in f t/sec g = acceleration due to gravity, 32.2 ft/sec2 B.2.3 Critical time The longest elapsed time before final how stoppage that will still permit this maximum pressure to occur is called the critical time; it is simply the total length that the pressure wave travels in one cycle, divided by the velocity ot the wave. It is given by the following equation : V = 21 Eq B3 in which, U -- the critical time, in seconds L = distance within the pipeline that the pressure wave moves before it is reflected back by a boundary condition, in feel a = velocity of the pressure wave in the line, in feet per second B.3 Valve Closure A valve in a water line may be of several different varieties, including gate, cone, and globe valves. When closing a valve, the area of the cross section of the pipeline that is pro gressively cut off is not generally proportional to the reduction in flow. In Fig. Bl, Graph 1 presents a plot CTO031444 " Fig. Bl. Time (Ti) = Effective for Full Cut Off Uniformly at Maximum Rate Reprinted by perminion of the Johnt-MnvilleSales Corporation. of stem travel versus flow in the line for three types of valves. Note that the first 30-40 percent of stem travel has little effect on the flow in the pipeline. B.3.1 Effective time. As stated previously, water hammer pressure is a function of the maximum rate of change of flow. Therefore, if tangents to the curves in Fig. Bl are drawn at the fastest rate of change (or steepest slope), the effective time of closure Te is obtained. (See the curves in Fig. Bl with tangents plotted and values of 7T determined.) This effec tive time, Te, is the time that is used in water hammer calculations. In most cases, it is about one half of the actual valve closing time. This indicates that if the critical time of a certain installed valve is calculated from Eq B3 and found to be x scioikK then the actual time for complete valve closure which will cause iii.im- munt pressure to occur will be ap proximately 2x seconds B.3.2 Relation to coairol la the design of a water system one ul the major consideration- hi 111< h- lion of a pipe is the design inn in.b CTD031445 B4 APPE.VD1X B pressure that the pipe will he required to carry in service. The design interna! pressure is the operating pressure plus the water hammer pres sure. In order to keep the water hammer or surge pressures at a con trolled level, calculations must he made to determine the valve closure times that will be required to stay within the design pressure level. B.3.3 Determining effective time. Figure B1 presents a convenient three-step method for determining effective valve closure times for a given percentage of the maximum pressure (surge pressure when valve is closed in less than the critical time). 1. Determine the pipeline constant K given by K=~ Eq B4 in which, K = pipeline constant a = velocity of the pressure wave in the line, in feet per second V = velocity of water in the flow line under normal conditions, in feet per second g = acceleration due to gravity, 32.2 ft/seC k,, = operating pressure in the line under normal conditions, in feet of water 2. Determine the maximum head that might be developed from the surge by employing the formula hmat = aV/g. 3. Determine the percentage of hna2 and find the corresponding effec tive closing time shown on the horizontal axis. This is given in units of 2L/a, which represents the critical time for the pipeline. Note that the time determined is the effective closing time and the actual time of valve stem travel is about twice as long. The reason for this is that the first half of the closing of the valve has little effect on the stoppage of the flow. It is the closing of the final half of the valve stem travel which closes off the-flow. The second half is the effective closing time. There fore, two times the effective closing time is the actual time of the valve stem travel. B.4 Pumped Systems In relation to water hammer and surge, the most important elements in a system are pumps and valves. In a gravity system only valves bat e to be considered. Both pumps and valves must be considered in a pumped system. B.3.I Complexity. The surge analy sis of a pumped system is more com plex than in a 100 percent gravity system because 1. In a pumped system, the prob lem begins in the slowing dowm of the rising water column when the pump is shut off (because of power failure or otherwise). Con sideration must be given to the time required for the pump to stop and for the flow to come to a halt. This involves the inertia of the motor and any flywheel in the assembly. Provisions nor mally should be made for slow opening and closing of pump control valves on pump systems. In a gravity system the hydraulic problem consists only of stopping the descending water column, 2. in a pumped system, the pipeline profile is usually irregular, with successive high and low points and with variable slopes. -These conditions may give rise to water c CTD031446 SECTION B.5 B5 column separation, causing se, vere surges and operational ' troubles. Surges from water column separation do not follow a standard pattern and they have been measured at many times the calculated values. B.4.2 Alternative layouts. The de sign of a pumped system may involve the consideration of alternative lay outs to keep surges and the consequent operational difficulties to a minimum. This work should be directed toward reducing the magnitude of surges and toward reducing the risk of water column separation that may be caused by the shutdown of a pump. : B.4.3 Water column separation. j Water column separation can be : serious due to the large magnitude of ^ the surges developed when the water [ column rejoins. It can occur 1. At pump locations at the start of ' a steep main. 2. When the pressure at a high point falls below atmospheric and air enters the line through air valves that may be located at a high point. 3. When the pressure falls to below the vapor pressure of water. 8.4.4 Entrapped air. Water col umn separation can cause difficulties, not only because of the before-men tioned surges set up by the rejoining of the water column, but because of the difficulties in getting air out of the line on subsequent start-up, even with air valves. Entrapped air can cause flow fluctuations and can seri ously reduce the capacity of the .system. B.S Methods of Control The two types of surge to be con trolled are negative surge and positive surge. The type is determined, of course, by whether the surge pressures developed are below or above the normal static level. B.5.1 Negative surges. Negative surges in themselves are usually not dangerous, except when they cause water column separation. If this occurs, extremely high positive surges result when the cavity closes, and this frequently causes serious prob lems. Tlie control of both negative and positive surges should be given consideration. B.S.2 Surge control devices. Limit ing negative and positive surges is accomplished by several types of surge control devices, as follows: 1. Controlled valves. This is one of the most effective means for controlling positive surges. As explained previously, the rate of opening and closing of a valve can be calculated to allow an acceptable level of surge. 2. Flywheel on pump motor. In the event of a power outage the inertia of the flywheel will keep the pump running for a period of time, during which it will gradually slow to a stop. This means that the water column in the pipeline will also be brought to a gradual stop, thus reducing the risk of water column separation. 3. Standpipe. This is generally a tank with the surface of the water at atmospheric pressure. It is, therefore, only practical at low heads. At a pump stoppage and consequent re duced pressure, the reserve of water in the tank flows into the pipe and reduces the risk of water column separation. For positive surge control the tank ~'IRwr 11 'i CTD031447 B6 APPENDIX B provides an outlet for the built-up pressure in the system. 4. Air vessel or surge tank. This is an enclosed vessel containing air and water. It functions similarly to a standpipe, with water reentering the line during negative surge and lea\ ing dur ing positive surge. The major difference is that the air in the vessel is under pressure and much higher heads can be em ployed in the pipe system. 5. One-way surge tank. This is an adaptation of the surge tank. It contains a check valve that permits water to enter the line during negative surge, but will not permit water to leave during positive surge. It is, therefore, only for control of negative surges and is very effective. 6. Reservoir of water. This is similar to the one way surge tank, but provides some control of positive surge by permitting the slow entrance of water into the reservoir during a positive surge. 7. Suction pipe. This is a bypass around the pump from the suction side. It contains a check valve to prevent backflow into the reservoir. It effec tively reduces negative pressure adjacent to the pump. 8. Surge relief valve. This is used for controlling positive and negative surges. The valve opens at a certain pressure and discharges water to relieve a surge; positive or negative. It must be carefully designed and controlled in order to be effective. 9. Nonreturn valve. This is a check, strategically placed in a line, that can bring a small mea sure of relief to positive pres sure However, unless properly placed, it can lead to higher rather than low er surge. 10. Reversal of pump. At pump stoppage the column of water reverses itself. If the pump will not run backwards to permit water to flow back through it, then positive surges will be developed by the sudden slop ping of the backflowing column of water. The pump should be designed to run reversed with out damage to itself. Design of pumps that can run reversed without damage, is a significant problem. Other measures may hav e to be taken. B.5.3 Economic considerations. From an economic standpoint it is usually worthwhile to properly evalu ate the surge potential in a system under design. The cost o! control devices may be balanced against the added strength of pipe, valv es. and other equipment that will be needed if surges are not controlled, and the most advantageous conclusion reached. Manufacturers of surge con trol equipment or consultants in this field should be sought for advice in complex situations. B.6 Surge Calculation Example The following example problem illustrates the calculation that maybe followed to determine valve closing time for the control ol surge within prescribed limits. A 24-in gravity transmission line is to operate at a pressure of 100 psi. Velocity in the line is to be 5 ft 'sec. A valve is to be included in the line at a distance of 5000 fi from the reservoir. If positive surge pressure CTD031448 SECTION B.7 B7 is to he controlled within SO psi, determine the minimum time for valve closure. Assume that the effective closing time is one half of the actual valve stem travel time. (E for as bestos-cement pipe = 3.4 X 106, wall thickness is 1.5 in., k for water = 3 X 10s) actual valve stem travel time would be twice this amount, or 17.4 sec. This calculated time (17.4 sec.), therefore, represents the fastest allowable time the valve can be closed in order to keep the surge pressure below the desired control level of 50 psi. Solution 1. Determine surge wave velocity 4660 I kd V1 +Ee 4660 1 + .1 X IQ X 24 3.4 X 10* X 1.5 = 3000 it/sec. 2. Determine maximum surge pres sure if the valve closes within the critical time a V 3000 X 5 ~T ~ 32.2 = 465 ft of water (200 psi) 3. Determine the critical time 2 X 5000 = 3.33 sec a 3000 4. Determine Constant K for use in Graph 2 (Fig. Bl) _ aV _ 3000 X 5 _ ~ 2ghQ~ 2 X 32.2 X 231 ~ ' 5. Determine percent of maximum surge pressure that should not be exceeded in the system. r--50 X 100 = 25 percent 6. Enter Graph 2 (Fig. Bl) with percent of hmax (25 percent). Go horizontally to the curves where K = 1.0. Read the effective clos ing time along the horizontal axis. This value is 2.6 and is given in units of 2L/a seconds. The effective closing time in seconds would be 2L/a X 2.6 = 3.33 X 2.6 = 8.7 sec. The B.7 Air in Pipelines Air in pipelines can cause serious operational difficulties, including re duction in capacity because of re duced cross-sectional area, and fluctu ation in flow caused by expanding and contracting air in the line. These fluctuations in flow cause sudden movements of the air from one loca tion to another, followed by slugs of water, and this can cause serious surges. B.7.1 Entrance oj air. Air can enter a pipeline in many ways. It may enter at the intake. Entry may be caused by release of air from water due to temperature and pressure variation, or it may be caused by draining the line, or by draining parts of the line during normal shut-down. Negative surges may cause air to enter at air valves. Air should be prevented from entering the line in the first place. This is very important in order to reduce operational diffi culties. Suggested solutions for con trol are as follows: 1. Intake. Correct design pro cedures, provide low water-level pump cut-off. 2. Release of air. Air is entrained in the water at intake and its release cannot be prevented. However, the quantities are not large and provisions for exhaust ing can be made by means of air valves. There are various types of air valves with different B8 APPEXOIX B functions, and the selection of the proper type and location for installation is essential. 3. Draining the line. Air cannot be prevented from entering the line on draining, of course. Large orifice air valves should be pro vided for exhausting the air during refilling. Draining and then refilling does not often oc cur; therefore, long filling times may be satisfactory. 4. Drainage during shut down. This can be a serious problem. Open standpipes can be pro vided for air entry and exhaust. Sweeping air out using high velocities is also a method. 5. Negative surges. The best way to prevent air front entering under these conditions is to de sign out the possibility of water column separation. Large vol umes of air may be involved here and can cause serious problems. Any one of the negative surge control devices described in para graph B.5.2 w'ill normally be adequate. B.7.2. Recommendations to combat air entrapment. Colorado State Uni versity has conducted studies to determine the effect of air entrapment in pipelines. The result of the studies proved that suddenly released en trapped air, under apparently static conditions, creates a situation similar to that of classic water hammer. Pressures are generated which may be on the order of fifteen times the pipeline test pressure. Any pipeline material is seriously affected by this rapid magnitude of load increase. Hydrostatic failure due to defective pipe may in all probability be traced to suddenly released entrapped air. The initial filling and testing of a pipeline is often the most critical period of its service life. Recom mendations to combat air entrapment were made as follows: 1. Pipeline should be laid to grade wherever possible. 2. Automatic continual acting air release valves should be used at all high points. 3. Air should be bled from pipeline slowly. 4. Limit filling velocity in the pipe line to one foot per second or less. 5. Use d/D = 1/10 to 1/100. d = diameter of air release valve D = pipe diameter The results of this study, together with the recommendations, have been found to be most useful to contractors in performing pipeline tests. Such rec ommendations also hat e been found to be useful to engineers from the standpoint of designing pipelines to minimize air problems. Appendix C Frictional Power Requirements This appendix is far information only and is not a part of A IVH'A C7Q0, 1 | The chart shown in Fig. Cl permits | rapid calculations of the yearly power ' costs to overcome friction loss of head. This chart is based on continuous pumping operation (24 hours per day and 365 days per year), a power cost of SO.01 per kwhr, and a motor-pump efficiency of 100 percent. For actual , operating conditions and local power j costs, appropriate factors must be apj plied to the values shown in the chart. ; By calculating power costs to over come friction in two pipe sizes, or for two different types of pipe having different flow coefficients, an annual power cost savings can be determined. Economic justification for going to a larger pipe diameter with lower annual power costs can be determined by establishing the present worth of the annual savings using Table Cl, which is based on the discounted cash flow method. If the present worth of the annual savings based on established interest rates exceeds the added costs for the installation of a different size or type of material, then economic justification exists for the added capital expenditure. Nomograph values for Fig. Cl are based on the following: Cost per 1000 ft of pipe per year--in doiJars Power cost--l<f per kilowatt hour Motor-pump efficiency (combined)--100 percent Friction coefficient C = 140 Continuous operation Note : Yearly power cost values derived in Fig. Cl are for coefficient of flow C = 140. They may be con verted to yearly power cost values for other coefficients of flow by means of the following multiplying factors: 1.15 for C = 130 1.34 for C= 120 1.57 for C = 110 1.86 for C = 100 2.26 for C = 90 2.83 for C = 80 4.82 for C = 60 Diameters derived from Fig. Cl are for coefficient of flow C = 140. These may be converted to other diameters for other coefficients of flow by means of the following multiplying factors: 1.033 for C = 130 1.063 /or C = 120 1.100 for C = 110 1,142 for C = 100 1.185 for C = 90 1.261 for C = 80 U65 for C = 60 ) f i ci '.STffTi-: CTD031451 C2 ui 'jaisuJBiQ adfd CTD031452 FIGURE Cl CTD031453 Mg C4 APPENDIX C Table Cl * Apply the following formula to Table Cl, Present Worth of an Income, of $1.00 per Year for the Next N Years: (1 -rr) -l r(l -f r)K where r = rate of yield in percent N -- number of years from present Example: When using a 10 percent rate of yield, an income of SI.00 occurring each year for the next 5 years has a * This table is reprinted by permission of the Johns-Manville Sales Corporation from their publication, "Discounted Cash Flow Method of Investment Appraisal." present worth of S3.791 ; for the next 7 years, $4,868; for the next 10 years, $6.145; etc. The present worth (PW) of a regular pattern of savings in the future is found as follows . Total years of operation -- 25 Amount of annual savings-- $5000.00 PW factor at 10 percent--9.077 Total present worth (PW) -- $45,385.00 When expenditure, cash income, and life are known, and income is the same each year, the PW factor can be computed by dividing expenditure by annual cash income. Yield can then be determined by looking for the factor on the line or known life in Table Ct. < ( CTD031454 TABLE Cl C5 TABLE Cl Present Worth of an Income of $1.00 per Year for the Next >< Years Tm .3% 1.0% LJ% 2.0% 2.3% 2.0% 15% 4.0% 4.5% 5.0% Tr> 1 .995 .990 .965 .980 .976 2 1.985 1.970 1.956 1.91*2 1.927 3 2.970 2.91a 2.912 2.881* 2.856 1* 3.950 3.902 3.851* 3.806 3.762 5 1* .926 1*.853 L.783 1*. 7X3 1*.61*6 6 5.896 5.795 5-697 5.601 5.508 7 6.862 6.728 6.598 6.1*72 6.31*9 a 7.823 7.652 7-1*86 7.325 7.170 9 8.779 8.566 8.361 8062 7.971 10 9.730 9-1*71 9.222 8.983 8.752 n 10.68 10.37 10.07 9.787 9.511* 12 11.62 11.26 10.91 10.58 10.26 13 12.56 12.13 11.73 11.35 10.98 ill 13.1*9 13.00 12.51* 12.11 11.69 15 11*.1*2 13.87 13.31* 12. 12.38 .971 1.913 2.829 3.717 1*.580 .966 1.900 2.802 3.673 l*.5l5 .962 1.886 2.775 3.630 i*.l*52 .957 1.673 2.71*9 3.588 1*. 390 .952 1.859 2.723 3.51*6 L.329 5.ia7 6.230 7.020 7.786 8.530 5.329 6.115 6.871* 7.608 8.317 5.21*2 6.002 6.733 7.1*35 8.111 5.158 5.893 6.596 7.269 7.913 5-076 5.766 6.1*63 7.108 7.722 9-253 9.951* 10.61* 11.30 11.91* 9.002 9.663 10.30 10.92 11.52 8.760 9.385 9.986 10.56 11.12 8.529 9.119 9.683 10.22 10.71* 8.306 8.863 9.391* 9.899 10.38 1 2 3 1* 5 6 7 8 9 10 11 12 13 11* 15 16 15.31* ll*.72 11*. 13 13.58 13.06 17 16.26 15.56 11*.91 11*.29 13.71 18 17.17 16.1*0 15.67 Hi.99 li.35 19 16.08 17.23 16.1*3 15.68 11*.98 20 18.99 18.05 17.17 16.35 15.59 21 19.89 18.86 17.90 17.CH 16.19 22 20.78 19.66 18.62 17-66 16.77 23 2Ji 21.68 20.1*6 19.33 18.29 17.33 22.56 21.21* 20.03 18.91 17.89 25 23.1*5 22.02 20.72 19.52 18.1*2 12.56 13.17 13.75 11*.32 Hi.88 12.09 12.65 13.19 13.71 11*.21 11.65 12.17 12.66 13.13 13.59 11.23 11.71 12.16 12.59 13.01 10.81* 11.27 11.65 12.09 12.1*6 15.1*2 15.91* 16.1*1* 16.91* 17.ia ll*.70 15.17 15.62 16.06 16.1*8 31*.03 11* .1*5 lit.86 15.25 15.62 13.la 13.78 H*.1S 11*.50 11*. 83 12.82 13.16 13.1*9 13.60 11*.09 16 17 18 19 20 21 22 23 21* 25 26 21*.32 22.80 21.1*0 20.12 18.95 17.88 16.89 15.98 15.15 11*.38 26 27 25.20 23.56 22.07 20.71 19.1*6 18.33 17.29 16.33 15.1*5 11*.61* 27 II 28 26.07 21*.31 22.73 21.28 19.97 29 26.93 25-07 23.38 21.81* 20.1*5 18.76 17.67 16.66 15.71* 11*.90 28 19.19 18.01* 16.98 16.02 15.11* 29 30 27.79 25.81 21*. 02 22.1*0 20.93 19.60 18.39 17.29 16.29 15.37 30 31 28.65 26.51* 21*.65 22.91* 21.1*0 32 29.50 27.27 2S.27 23.1*7 21.85 33 30.35 27.99 25.88 23.99 22.29 31* 31.20 28.70 26.1*8 21*.50 22.72 35 32.01* 29.1a 27.08 25.00 23.15 20.00 20.39 20.77 21.13 21.1*9 18.71* 19.07 19.39 19.70 20.00 17.59 17.87 18.15 18. ia 18.67 16.51* 16.79 17.02 17.25 17.1*6 15.59 15.80 16.00 16.19 16.37 31 32 33 31* 35 36 32.87 30.11 27.66 25.1*9 23.56 37 33.70 30.80 28.21* 25.97 23.96 38 31*. 53 31.1*9 28.81 26.1*1* 21*.35 39 35.35 32.16 29.37 26.90 21*. 73 ItO 36.17 32.81* 29.92 27.36 25.10 111 li2 36.99 33.50 30. **6 27.80 25.1*7 37.80 31.16 30.99 28.21* 25.82 1*3 liii 38.61 31*. 81 31.52 28.66 26.17 39.1*1 35.1*6 32.01, 29.08 26.50 1*5 1*0.21 36.09' 32.55 29.1*9 26.83 1*6 1*7 1*1.00 Ll.79 36.73 37.35 33.06 33.55 29.89 30.29 27.15 27.1*7 1*8 1*2.58 37.97 3l*.oi* 30.67 27.77 1*5 1*3.36 38.59 31*. 53 31.05 28.07 50 1*1*.11* 39.20 35.00 31.1*2 28.36 21.83 22.17 22.1*9 22.81 23.12 20.29 20.57 20.81* 21 ao 21.36 18.91 19.U, 19.37 19.58 19.79 17.67 17.86 18.05 18.23 18.1*0 16.55 16.71 16.67 17.02 17.16 23.ia 23.70 23.98 21*. 25 21*. 52 21.60 21.81* 22.06 22.28 22.50 19.99 20.19 20.37 20.55 20.72 18.57 18.72 18.87 19.02 19.16 17.29 17.1*2 17.55 17.66 17.77 21*.78 25.03 25.27 25.50 25.73 22.70 22.90 23.09 23.28 23.1*6 20.89 21.01* 21.20 21-31* 21.1*8 19.29 19.1*2 19.51* 19.65 19.76 17.88 17.96 18.08 18.17 18.26 36 3? 38 39 1*0 ia 1*2 1*3 1*1* 1*5 1*6 1*7 1*8 1*9 50 CTD031455 V C6 TABLE Cl TABLE Cl (continued) Ywi 5 J* 6.0% 6 5% 7.0* 7.J* 8.0* S.tt 9.0% 9.3% 10.0* 1 .918 .913 .939 .935 .930 .926 .922 .917 .913 .909 1 2 1.816 1.833 1.821 1.808 1.796 1.783 1.771 1.759 1.717 1.736 2 , 2.696 2.673 2.616 2.621 2.6C1 2.577 2.551 2.531 2.509 2.187 3 ici 3.505 3.165 3.126 3.387 3-319 3.312 3.276 3.21,0 3.201 3.170 1.270 *,.212 1.156 1.100 1.016 3.993 3.91a 3.870 3.810 3.791 1 5 fc 1.996 1.917 1.811 1.767 1.691 1.623 1.551 1.2,86 1.120 1.355 6 7 5.683 5.562 5.185 5.389 5.297 5.206 5.119 5.033 1.950 1.868 7 e 6.335 6.210 6.089 5.971 5.857 5.717 5.639 5.535 5.133 5.335 8 9 6.952 6.802 6.656 6.515 6.379 6.217 6.119 5.995 5.875 5.759 9 10 7.538 7.360 7.189 7.021 6.861 6.710 6.561 6.118 6.279 6.115 10 n 8.093 7.887 7.689 7.199 7.315 7.139 6.969 6.805 6.617 6.195 11 12 8.619 8.381 8.159 7.913 7.735 7.536 7.315 7.161 6.981 6.811 12 u 9.U7 6.853 8.600 8.358 8,126 7.901 7.691 7.187 7.291 7.103 13 iii 9.590 9.295 9.011 8.715 8.189 8.211 8.010 7.786 7.572 7.367 11 15 10.01 9.712 9.103 9.108 8.827 8.559 8.301, 8.061 7.628 7.606 15 16 10.16 10.U 9.768 9.117 9.112 8.851 6.575 8.313 8,062 7.821 16 17 10.87 10.18 10.11 9.763 9.131 9.122 8.825 8.511 8.276 8.022 17 18 n.25 10.83 10.13 10.06 9.706 9.372 9.055 8.756 8.171 8.201 18 19 11.61 11.16 10.71 10.31 9.959 9.601 9.268 8.950 8.650 8.365 19 20 11.95 11.17 11.02 10.59 10.19 9.818 9.163 9.129 8.812 8.511 20 a 12.28 11.76 11.29 10.81 10.11 10.02 9.611 9.292 8.961 8.619 a 22 12.56 12.01 11.51 11.06 10.62 10.20 9.810 9.112 9.097 8.772 22 23 12.88 12.30 11.77 11.27 io. eo. 10.37 9.963 9.580 9.2a 8.883 23 2ii 13.15 12.55 11.99 11.17 10.98 10.53 10.10 9.707 9.331 8.985 21 25 13.11 12.78 12.20 11.65 11.15 10.68 10.23 9.823 9.138 9.077 25 26 13.66 13.00 12.39 11.83 11.30 10.81 10.35 9.929 9.532 9.161 26 27 13.90 13.21 12.58 11.99 11.11 10.91 10.1,7 10.03 9.618 9.237 27 26 11.12 13.11 12.75 12.11 11.57 11.05 10.57 10.12 9.697 9.307 28 29 11.33 13.59 12.91 12.28 11.70 11.16 10.66 10.20 9.769 9.370 29 30 11.53 13.77 13.06 12.11 11.81 11.26 10.75 10.27 9.835 9.127 30 31 11.72 13.93 13.20 12.53 11.92 11.35 10.83 10.31 9.895 9.179 31 32 U.90 11.OS 13.33 12.65 12.02 n.n 10.90 10.11 9.950 9.526 32 33 15.06 11.23 13.16 12.75 12.11 11.51 10.97 10.16 10.00 9.569 33 31 15.21 11.37 13.58 12.85 12.19 11.59 11.03 10.52 10.05 9.609 31 35 15.39 11.50 13.69 12.95 12.27 11.66 11.09 10.57 10.09 9.611 35 36 15.51 11.62 13.79 13.01, 12.35 11.72 11.11, 10.61 10.13 9.677 36 37 15.67 11.71 13.89 13.12 12.12 11.78 11.19 10.65 10.16 9.706 37 38 15.61 11.85 13.98 13.19 12.18 11.83 11.21, 10.69 10.19 9.733 38 39 10 15.93 11.95 11.07 13.27 12.51 16.05 15.05 11.15 13.33 12.59 11.88 11.28 10.73 10.22 9.757 11.93 11.32 10.76 10.25 9.779 39 10 ia 12 13 16.16 16.26 16.36 15.11 15.23 15.31 11.22 11.29 11.36 13.39 13.15 13.51 12.65 12.69 12.71 11.97 U.35 10.79 10.27 9.799 12.01 11-38 10.80. 10.29 9.817 12.01, n.ia 10.81 10.31 9.831 11 12 13 11 16.16 15.38 11.12 13.56 12.78 12.08 u.ll 10.86 10.33 9.819 11 15 16.55 15.16 11.18 13.61 12.82 12.11 11.17 10.88 10.35 9.863 15 16 16.63 15.52 11.51 13.65 12.86 12.11, u.19 10.90 10,36 9.875 16 17 16 16.71 15.59 11.59 13.69 12.89 16.79 15.65 11.61 13.73 12.92 12.16 u.5i 10.92 10.38 9.887 12.19 u.53 10.93 10.39 9.897 17 18 19 16.86 15.71 11.68 13.77 12.95 12.a 11.55 10.95 10.10 9.906 19 50 16.93 15.76 11.73 13.80 12.98 12.23 11.57 10.96 10.11 9.915 50 TABLE Cl C7 Years 10.5* 11.0* TABLE Cl (continued) 11.3* 120* 12. J* 13.0* 13.5* 14.0* U.5* 15.0* Yon 1 .905 .901 .697 .893 .869 2 1.728 1.713 1.701 1.690 1.679 3 2.865 2.888 2.823 2.802 2.361 8 3.136 3.102 3.070 3.037 3.006 5 3.783 3-696 3.650 3.605 3.561 . 8C5 1.668 2.361 2.978 3.517 .881 1.657 2.381 2.988 3.875 . e77 1.687 2.322 2.918 3.833 .873 1.636 2.302 2.868 3.392 .870 1.626 2.283 2.655 3.352 1 2 3 8 5 6 8.292 8.231 8.170 8.111 8.058 7 8.799 8.712 8.637 8.568 8.892 8 5.239 5.186 5.056 8.968 8.882 9 5.686 5.537 5.831 5.328 5.228 10 6.015 5.889 5.768 5.650 5.536 3.998 8.823 8.799 5.132 5.826 3.983 8.355 8.718 5.038 5.320 3.889 8.288 8.639 8.986 5.216 3.836 8.228 8.562 8.858 5.116 3.788 8.160 0.887 8.772 5.019 6 7 8 9 10 11 6.388 6.207 6.070 5.938 5.810 12 6.650 6.892 6.381 6.198 6.053 13 6.923 6.750 6.583 6.828 6.270 18 7.170 6.982 6.801 6.628 6.862 15 7.398 7-191 6.997 6.811 6.633 5.687 5.918 6.122 6.302 6.862 5.568 5.787 5.979 6.189 6.299 5.853 5.660 5.882 6.002 6.182 5.381 5.538 5.710 5.861 5.992 5.238 5.821 5.583 5.728 5.887 11 12 13 18 l-S 16 7.596 7.379 7.172 6.978 6.785 17 7.779 7.589 7.329 7.120 6.920 18 7.985 7.702 7.870 7.250 7.080 19 8.095 7.839 7.596 7.366 7.187 20 e.231 7.963 7.710 7.869 7.281 6.608 6.729 6.880 6.938 7.025 6.831 6.587 6.689 6.739 6.819 6.265 6.373 6.867 6.550 6.623 6.106 6.206 6.298 6.370 6.837 5.958 6.087 6.128 6.198 6.259 16 17 18 19 20 21 8.358 6.075 7.811 7.562 7.326 22 8.865 8.176 7.903 7.685 7.801 23 8.566 8.266 7.988 7.718 7.867 28 8.657 6.386 8.058 7.788 7.526 25 3.739 6.822 8.128 7.883 7.579 7.102 7.170 7.230 7.283 7.330 6.889 6.951 7.005 7-053 7.095 6.687 6.783 6.792 6.835 6.873 6.895 6.586 6.590 6.629 6.663 6.312 6.359 0.399 6.838 6.666 21 22 23 28 25 26 8.818 6.886 6.163 7.896 7.626 27 6.881 8.588 8.236 7.983 7.667 26 6.982 8.602 8.283 7.988 7.708 29 8.997 8.650 8.326 8.022 7.737 30 9.087 8.698 8.368 8.055 7.766 31 9.093 6.733 6.398 8.085 7.792 32 9.138 8.769 8.829 8.112 7.815 33 9.171 8.801 8.856 6.135 7.636 38 9.208 8.829 8.861 3.1S7 7.858 35 9.235 8.855 8.503 8.176 7.670 36 9.262 8.879 8.523 8.192 7.835 37 9.287 8.900 8.581 6.208 7.898 38 9.309 8.919 8.557 8.221 7.909 39 9.330 8.936 8.571 8.233 7.919 80 9.388 8.951 5.538, 8.288 7.928 81 9.365 8.965 8.595 6.253 7.936 82 9.380 8.977 8.606 6.262 7.983 83 9.398 8.989 8.615 8.270 7.989 88 9.806 8.999 6.623 8.276 7.955 85 9.U7 9.008 8.631 8.283 7.960 86 9.827 9.016 8.637 8.288 7.965 87 9.837 9.028 8.683 8.293 7.968 88 9.885 9.030 8.689 8.297 7.972 89 9.852 9.036 8.658 8.301 7.975 50 9.859 9.082 8.658 8.308 7.978 7.372 7.809 7.881 7.870 7.896 7.132 7.165 7.198 7.219 7.282 6.906 6.935 6.961 6.983 7.003 6.693 6.718 6.781 6.761 6.778 6.691 6.518 6.538 6.551 6.566 7.516 7.536 7.556 7.572 7.566 7.261 7.279 7.298 7.307 7.319 7.020 7.035 7.088 7.060 7.070 6.793 6.806 6.817 6.827 6.836 6.579 6.591 6.600 6.609 6.617 7.598 7.609 7.618 7.627 7.638 7.330 7.339 7.387 7.358 7.361 7.079 7.087 7.098 7.100 7.105 6.888 6.851 6.856 6.861 6.866 6.623 6.629 6.636 6.638 6.682 7.681 7.687 7.652 7.657 7.661 7.366 7.371 7.375 7.379 7.383 7.110 7.118 7.117 7.120 7.123 6.870 6.873 6.876 6.879 6.881 6.685 6.688 6.650 6.652 6.658 7.668 7.668 7.671 7.673 7.675 7.386 7.380 7.390 7.392 7.398 7.126 7.120 7.130 7.131 7.133 6.883 6.685 6.836 6.687 6.889 6.656 6.657 6.659 6.660 6.661 26 27 28 29 30 31 32 33 38 35 36 37 38 3890 81 82 83 88 85 86 87 88 89 50 C8 APPENDIX C TABLE Cl (continued) Yrti 15.5% 16.0% 16.9% 17.0% 17.3% 1 .866 .062 .858 .855 .651 2 1.615 1.605 1.595 1.585 1.575 3 2.261* 2.21*6 2.228 2.210 2.192 4 2.826 2.798 2.770 2.71*3 2.716 5 3.313 3.271* 3.236 3.199 3.163 *.0% K.3% 19.0% i?.n 2.0% Ymm1 .81*7 1.566 2.171* 2.690 3.127 .81*1* 1.556 2.157 2.661* 3.092 .81*0 1.51*7 2.11,0 2.639 3.058 .837 1.537 2.123 2.613 3.021* .833 1.528 2.106 2.589 2.991 1 2 3 4 5 6 3.731* 3.685 3.636 3.589 3.51*3 7 1*.099 1*. 039 3.980 3.922 3.866 8 1*.1*15 1*. 31*1* l*.271i 1*.207 l*.ll*2 9 1*. 688 1*.607 i*.527 4.1*51 i*.376 10 1*. 925 1*. 633 1*. 71*5 U. 659 !*.575 3.1*98 3.612 li.078 1*.303 1*. 1*91* 3.1*53 3.758 U.015 1*.232 4.415 3.410 3.706 3.951* 1*.163 1*.339 3.367 3.655 3.895 4.096 1.26S 3.326 3.605 3.837 It.031 lt.192 6 7 6 9 10 11 5.130 5.029 1*.931 I1.836 It.71*5 12 5.307 5.197 5.091 1*.988 1*.689 13 5.1*61 5.31*2 5.226 5.U8 5.012 14 5.591* 5.1*68 5.31*6 5.229 5.117 15 5.709 5.575 5.1*1*7 5.321* 5.206 1* .656 1*. 793 U.910 5.008 5.092 lt.570 1*.700 1*. 810 4.903 4.982 1*.1*86 It.611 4.715 It.802 lt.876 It.1*06 U.523 It.622 4.705 lt.771* it.327 4.439 4.533 It.611 4.675 11 12 13 14 15 16 5.808 5.668 5.531* 5.1*05 5.281 17 5.895 5.71*9 5.609 5.1*75 5.31*6 18 5.969 5.818 5.673 5.531* 5.1*01 2019 6.031* 5.877 5.728 5.581* 5.1*1*7 6.090 5.929 5.775 5.628 5.1*87 5.162 5.222 5.273 5.316 5.353 5.01,8 5.101* 5.151 5.191 5.221* 4.938 U.990 5.033 5.070 5.101 4.832 lt.880 4.921 4.954 4.983 4.730 4.775 4.812 4.843 4.870 16 17 16 19 20 21 6.139 5.973 5.815 5.665 5.521 22 6.181 6.011 5.850 5.696 5.550 23 6.217 6.01*1* 5.880 5.723 5.571* 24 6.21*9 6.073 5.905 5.71*6 5.595 25 6.276 6.097 5.927 5.766 5.613 5.381* 5.1*10 5.1*32 5.1*51 5.1*67 5.252 5.276 5.296 5.313 5.328 5.127 5.11*9 5.167 5.182 5.195 5.007 5.026 5.01*3 5.057 5.069 4.891 4.909 4.925 4.937 4.948 21 22 23 24 25 26 6.299 6.118 5.91*6 5.783 5.628 27 6.320 6.136 5.962 5.798 5.6U 28 6.337 6.152 5.976 5.810 5.652 29 6.353 6.166 5.988 5.820 5.661 30 6.366 6.177 5.999 5.829 5.669 31 6.378 6.187 6.007 5.837 5.676 32 6.387 6.196 6.015 5.81*1* 5.681 33 6.396 6.203 6.021 5.81*9 5.686 31* 6.1*01* 6.210 6.027 5.851 5.691 35 6.1*10 6.215 6.032 5.858 5.691* 36 6.1*16 6.220 6.036 5.862 5.697 37 6.1*20 6.221* 6.039 5.865 5.700 38 6.1*25 6.228 6.01*2 5.867 5.702 39 6.1*28 6.231 6.015 5.869 5.701* 1*0 6.1*31 6.233 6.01*7 5.871 5.705 1*1 6.1*31* 6.236 6.01*9 5.873 5.707 1*2 6.1*36 6.238 6.051 5.871* 5.708 1*3 6.1*38 6.239 6.052 5.875 5.709 1*1* 6.1*1*0 6.21*1 6.053 5.876 5.710 1*5 6.1*1*2 6.21*2 6.051 5.877 5.710 1*6 6.1*1*3 6.21*3 6.055 5.878 5.711 1*7 1*6 6.1*1*1* 6.21*1* 6.056 5.879 5.711 6.1*1*5 6.21*5 6.057 5.879 5.712 1*9 6.1*1*6 6.21*6 6.057 5.880 5.712 50 6.1*1*7 6.21*6' 6.058 5.880 5.712 5.1*80 5.1*92 5.502 5.510 5.517 5.31*0 5.350 5.359 5.366 5.372 5.206 5.215 5.223 5.229 5.235 5.078 5.086 5.093 5.099 5.101* 4.956 4.964 4.970 4.975 4.979 26 27 28 29 30 5.523 5.528 5.532 5.536 5.539 5.377 5.382 5.385 5.389 5.391 5.239 5.21*3 5.21*6 5.249 5.251 5.108 5.111 5.111, 5.116 5.118 4.982 4.965 4.988 4.990 4.992 31 32 33 34 35 5.SU1 5.51*3 5.51*5 5.51*7 5.51*8 5.393 5.395 5.397 5.398 5.399 5.253 5.255 5.256 5.257 5.258 5.120 5.121 5.122 5.123 5.121* 4.993 4.994 4.995 4.996 4.997 36 37 38 39 40 5.51*9 5.550 5.551 5.552 5.552 5.1*00 5.1*01 5.1*02 5.1*02 5.1*03 5.259 5.260 5.260 5.261 5.261 5.125 5.125 5.126 5.126 5.127 4.997 4.998 4.998 4.998 4.999 5.553 5.553 5.551* 5.551* 5.551* 5.1*03 5.1*01* 5.1*01* 5.1*01* 5.1*01* 5.261 5.262 5.262 5.262 5.262 5.127 5.127 5.127 5027 5.128 4.999 4.999 4.999 4.999 4.999 41 42 43 44 45 46 47 48 49 50 Q { I ! f CTD031458 iKfc L i , _ l TABLE Cl C9 TABLE Cl fcontinued) 2Vrai 21* 22* 23* U% % 26* 27* 28* 29* 30* Ymti 1 2 3 a .826 1.509 2.071 2.510 .620 21..019122 2.191 .813 21..011711 2.118 .806 1.157 1.981 2.101 .800 1.110 1.952 2.362 5 2.926 2.661 2.803 2.715 2.689 6 3.215 3.167 3.092 3.020 2.951 87 3.508 3.116 3.327 3.212 3.ia 3.726 3.619 3.518 3.121 3.329 9 3.905 3.786 3.673 3.566 3-163 10 1.051 3.923 3.799 3.682 3.571 12u 1.177 1.035 3.902 3.776 3.656 1.278 1.127 3.985 3.851 3.725 13 1.362 1.203 1.053 3.912 3.780 11 1.132 1.265 1.106 3.962 3.821 15 1.189 1.315 1.153 1.001 3.859 16 1.536 1.357 1.189 1.033 3.887 17 18 19 20 1.576 1.608 1.635 1.657 1.391 1.119 1.112 1.160 1.219 1.213 1.263 1.279 11..005890 11..019170 3.910 3.928 3.912 3.951 21 22 1.675 1.690 1.176 1.188 1.292 1.302 1.121 1.130 3.963 3.970 23 1.703 1.199 1.3U 1.137 3.976 214 1.713 1.507 1.318 1.113 3.9a 25 1.721 1.511 1.323 1.117 3.985 1..172911 1.923 2.320 2.635 .787 1.107 1.896 2.280 2.583 .781 11..839628 2.2a 2.532 .775 1.376 1.8a 2.203 2.163 .769 1.361 1.816 2.166 2.136 2.885 3.083 3.2U 3.366 3.165 2.821 3.009 3.156 3.273 3.361 2.759 2.937 3.076 3.181 3.269 2.700 2.868 2.999 3.100 3.178 2.6a 2.802 2.925 3.019 3.092 3.5a 3.606 3.656 3.695 3.726 3.137 3.193 3.538 33..567031 3.335 3.387 3.127 3.159 3.183 3.239 3.286 3.322 3.351 3.373 3.117 3.190 3.223 3". 2a 3.266 3.751 3.771 3.786 3.799 3.008 3.623 3.610 3.651 3.661 3.673 3.503 3.518 3.529 3.539 3.516 3.390 3.103 3.a3 3.ai 3.a? 3.283 3.295 3.301 3.3U 3.316 3.816 3.822 3.827 3.831 3.831 3.679 3.681 3.689 3.692 3.691 3.551 3.556 3.559 3.562 3.561 3.132 3.W6 3.138 3.ia 3.ia 3.320 3.323 3.325 3.327 3.329 1 2 31 5 6 76 190 n 12 13 11 15 16 17 18 19 20 21 22 2213 25 26 1.728 1.520 1.328 1.151 3.988 27 1.731 1.521 1.332 1.151 3.990 28 1.739 1.528 1.335 1.157 3.992 29 1.713 1.531 1.337 1.159 3.991 30 1.716 1.531 1.339 1.160 3.995 n 1.719 1.536 1.3a 1.161 3.996 32 1.751 1.538 1.312 1.162 3.997 33 1.753 1.539 1.313 1.163 3.997 31 1.755 1.510 1.311 1.161 3.998 35 1.756 1.511 1.315 1.161 3.998 36 1.757 1.512 1.315 1.165 3.999 37 1.758 1.513 1.316 1.165 3.999 38 1.759 1.513 1.316 1.165 3.999 39 1.759 1.511 1.316 1.166 3.999 L0 1.760 1.511 1.317 1.166 3.999 lil 1.760 1.511 1.317 1.166 1.000 11U2 ii3 1.760 1.511 1.317 1.166 1.000 1.761 1.515 1.317 1.166 1.000 1.761 1.515 1.317 1.166 1.000 15 1.761 1.515 1.317 1.166 1.000 I46 1.761 1.515 1.318 1.166 1.000 17 1.761 1.515'' 1.318 1.166 1.000 118 1.761 1.515 1.318 1.167 1.000 ? 1.761 1.515 1.318 1.167 1.000 50 1.762 1.515 1.318 1.167 1.000 3.037 3.839 3.810 3.aa 3.812 3.696 3.698 3.699 3.700 3.701 3.566 3.567 3.568 3.569 3.569 3.111 3.115 3.116 3.116 3.117 3.330 3.331 3.331 3-332 3.332 3.813 3.811 3.811 3.815 3.8145 3.701 3.702 3.702 3.703 3.703 3.570 3.570 3.570 3.571 3.571 3.117 3.117 3.118 3.118 3.118 3.332 3.333 3.333 3.333 3.333 3.815 3.815 3.816 3.816 3.816 3.703 3.703 3.703 3.703 3.703 3.571 3.571 3.571 3.571 3.571 3.118 3.118 3.118 3.118 3.118 3.333 3.333 3.333 3.333 3.333 3.816 3.816 3.816 3.816 3.816 3.703 3.701 3.701 3.701 3.701 3.571 3.571 3.571 3.571 3.571 3.118 3.118 3.116 3.118 3.118 3.333 3.333 3.333 3.333 3.333 3.816 3.816 3.816 3.816 3.816 3.701 3.701 3.701 3.701 3.701 3.571 3.571 3.571 3.571 3.571 3.118 3.118 3.118 3.118 3.W;8 3.333 3.333 3.333 3.333 3.333 26 27 28 29 30 31 32 33 31 35 36 37 38 39 10 a a a 11 15 16 17 U8 So CTD031459 t 1P--25M--9/78--43403 J CTD031460