Document ZBL9pEbJvwOV76g041X9OGeyL

Tr 1 44 CHAPTER 4 1959 Guide ^5 * N ok \ \ > v. ir % CN \S V s / / /I 6-------53------53 04 oj u> PIPE OUKCTCPS 5-- iS u Fig. 17.... Location of Vena Confracta in Relation to Ratio of Orifice to Pipe Diameter and to Rote of Flow Variable Area Flow Meters For permanent installations where high precision, mwHness, and ease of operation are important, the variable area flow meter has proved very satisfactory. Its most frequent use is in measurement of liquids or gases in small diameter pipes. For ducts or pipes over 6 in. in diameter, the expense, of this meter may not be warranted. In large systems, how ever, the meter might be placed in a by-pass line and used in conjunction with an orifice. In its most common form, the variable area meter, Fig. 18, consists essentially of a float which is free to move vertically in a transparent tapered tube. The fluid to be metered enters at the narrow bottom end of the tube and moves upward, passing at some point through the annulus formed between the float and inside wall of the tube. At any particular rate of flow, the float assumes a definite position in the tube, its ready for installation. In such cases, the manufacturer's instructions should be followed with care in order to avoid serious errors. Further information on such systems is given in References 2, 3, and 5. Pitot Tube In certain cases, such as in rectangular ducts, it is impracti cable to use standard orifices, and consequently, either a specially designed orifice must be calibrated, or an inde pendent flow device must be used. In either case, the Pitot tube is useful. It consists essentially-of an innpr bent tube with its open end pointing upstream so as to measure total pressure, and an outer tube having small holes on the side for communicating static pressure to a manometer. (See Fig. 3, Chapter 44). The difference in'liquid level in the manometer will be proportional to the square of the velocity, for incom pressible flow, so that in general ........ V - vm (63) For compressible flow, the differential head is to be divided by the correction Fc from Equation 64, where Ft - 1 + %M* + (64) (65) In the use of a Pitot tube system, care is required in ob taining correct total and static pressures. The total pressure tube must be smoothly constructed, and should point di rectly upstream. The static pressure tap must be located so that local flow interferences will not reduce the value. In any case, it is better to obtain an independent calibration, or use a specially designed and manufactured probe. A number of such Pitot tube probes are available, and can be used without calibration. In using Pitot tubes to obtain flow rates, it is necessary to make a traverse of the pipe and thereby to obtain one of the profiles of Fig. 5. In rectangular ducts or near valves or fit tings, a disturbed flow pattern would be obtained, and there fore, in such cases, a fairly complete survey should be made. The flow in such cases will be computed from the average of the local velocities, as obtained by Equation 63. Rg. 18 .... Schematic Diagram of Variable Area Flow Meter location being indicated by means of a calibrated scale on the tube. The position of the float is established by a balance between the fluid pressure forces across the annulus and the weight of the float itself. The buoyant force which must support the float, Vf(p/ -- p), is balanced by the pressure difference acting on the cross-section area of the float, A/Ap, where pf, A, , o/t are, respectively, the float density, float cross-section area, and float volume. Accordingly, the difference in head across the annulus is given by Ap Vf{p, -- p) p Afp (66) The volume flow follows from Equation 53 as Q" and the mas3 flow as p)bAj (67) w " pQ 9 KAw/2gPf{pj -- p)-p/Af (68) The flow for any selected fluid is, accordingly, very nearly proportional to the area, so that a convenient calibration of RyidCFlow the tube may be obtained. The behavior of the flow coefficient, K has been investigated4 and the action of the flow meter as just outlined, experimentally ouiuii-med. The Sow coefficient variation for any float roust be known in order to use the meter for different fluids. Some developments have been carried on in the design of the float to reduce the variation of the flow coefficient with Reynolds number, and also with regard to float materials, to reduce the dependence of mass flow calibration on fluid density. This type of flow meter is usually furnished in standard sixes calibrated for specific fluids by the manufacturer. The compactness, reliability, and ease of installation are particu larly advantageous when many measurements of essentially the rajTM* type are to be made. LETTER SYMBOLS USED IN CHAPTER 4 0 -- ratio, throat or orifice diameter to pipe diameter. >i 9 absolute viscosity, pounds per foot second. p/p " kinematic viscosity, square feet per second. p = density of flowing fluid, pounds per cubic foot. pm = proper mean density, pounds per cubic foot. p = density of water at 60 F (62.37 lb per cubic foot). P! = density of float id variable area meters. 4 = expansion factor for nozzles. a -- velocity of sound, feet per second. A -- cross-sectional area of flow, square feet. C =* correction factor (coefficient of discharge) for flow through orifice, nozzle or Venturi. cp -- specific heat of gas at constant pressure. c, = specific beat of gas at constant volume. D diameter of fluid stream, feet, d = internal diameter of pipe, feet, ds 9 hydraulic diameter, feet. e = absolute roughness of pipe surface, feet. Ft 9 correction factor for differential head in compressible flow. / = dimensionless friction coefficient. g 9 gravitational acceleration, feet per (second) (second). gt 9 gravitational conversion factor " 32.174 (pounds mftAft per pound force) X feet per (second) (secood). h -- enthalpy, Btu per pound of fluid. h/ -- loss of head, feet of fluid. A, total head, feet of fluid. J -- mechanical equivalent of heat = 778 foot pounds per Btu. K 9 flow coefficient (correction factor), including velocity of approach correction factor, for flow through orifice, nozzle or Venturi. k 9 ratio of specific heat at constant pressure to specific heat at constant volume. L -- perpendicular distance from axis of pipe, feet. I 9 length of pipe, feet. 45 AT 9 Mach number. Na, 9 Reynolds number. p 9 pressure, pounds per square foot, p* 9 stagnation pressure, pounds per square foot, p, = critical pressure. Q 9 discharge rate, cubic feet per second. q 9 heat transferred to the fluid per pound of fluid flowing, Btu. R 9 gas constant, r radius of pipe, feet. * = entropy of fluid in Btu per (pound) (Fahrenheit de gree). T 9 temperature, absolute, Fahrenheit degrees, u 9 internal energy, Btu per pound of fluid. V 9 velocity, feet per second. Vt = critical velocity, feet per second. v 9 specific volume, cubic feet per pound. W 9 mechanical work per pound of fluid flowing, foot pounds. to 9 flow of gas, pounds per secood. Y 9 expansion factor (correcting for expansion of gas under reduced down-stream pressure). t 9 elevation above some arbitrary datum, feet. REFERENCES 1 L. F. Moody: Friction factors for pipe flow (ASME Trans actions, Vol. 66, 1944, p. 671, with discussion p. 678); also An approximate formula for pipe friction factors (Mechanical Engineering, Vol. 69, 1947, p. 1005). * American Society of Mechanical Engineers: Fluid Meters, Their Theory and Application (1937, 4th ed.). * American Society of Mechanical Engineers: Flow Measure ment, Power Test Codes, 1949, Part 5, Chapter 4. 4 National Advisory Committee for Aeronautics, NACA Tech. Mem. 952, 1940: Standards for Discharge Measurement (Translation of German Industrial Standard, 1932). * American Gas Association, Natural Gas Department: Gas Measurement Committee Report No. 2, 1948. * E. M. Schoenborn Jr. and A- P- Colburn: The flow mecha nism and performance of the rotameter (American Institute of Chemical Engineers Transactions, Vol. 35, 1939, p. 359). BIBLIOGRAPHY E. F. Obert: Thermodynamics (McGraw-Hill Book Co., 1948). ' N. A. Hall: Thermodynamics of Fluid Flow (Prentice Hall, 1951). R. A. Dodge and M. J. Thompson: Fluid Mechanics (McGraw-Hill Book Co., 1937). R. C. Binder: Fluid Mechanics (Prentice Hall, 2nd Ed., 1949). P. P. Ewald, H. Poschl and L. Praodtl: The Physics of Solide and Fluids (Blackie, 1936). Emory Kemler: A study of the data on the flow of fluids in