Document 9JqRwnqYwxyB4pLrQQO0J1Vp3

98 CHAPTER 4 1950 Guide and the mass flow as to = pQa = KAi\/2gV({pi -- p) p/A f (76) The flow for any selected fluid is accordingly very nearly proportional to the area so that a convenient calibration of the tube may be obtained. The behavior of the flow coefficient, K, has been investigated6 and the ac tion of the flow meter as just outlined, experimentally confirmed. The flow coefficient variation for any float must be known in order to use the meter for different fluids. Some developments have been carried out in the design of the float to reduce the variation of the flow coefficient with Reynolds number, and also on float materials to reduce the dependence of mass flow calibration on fluid density. This type of flow meter is usually furnished in standard sizes calibrated for specific fluids by the manufacturer. The compactness, reliability, and ease of installation are particularly advantageous when many measure ments of essentially the same type are to be made. LETTER SYMBOLS USED IN CHAPTER 4 . 0 = ratio, throat or orifice diameter to pipe diameter. n = absolute viscosity, pounds per foot second. /i/p = kinematic viscosity, square feet per second, p = density of flowing fluid, pounds per cubic foot. Pw = density of water at 60 F (62.37 lb per cubic foot). pt -- density of fluid over mercury in a manometer. tp = expansion factor for nozzles. 0 a* velocity of sound, feet per second. A = cross-sectional area of now, square feet. C = correction factor (coefficient of discharge) for flow through orifice, nozzle or Venturi. cp = specific heat of gas at constant pressure. cT ~ specific heat of gas at constant volume. D = diameter of fluid stream, feet. d = internal diameter of pipe^feet. e = absolute roughness of pipe surface, feet. / = dimensionless friction coefficient. g = gravitational acceleration, feet per (second) (second). ge = gravitational conversion factor = 32.174 (pounds mass per pound force) X feet per (second) (second). G ~ specific gravity of gas referred to air. h = enthalpy, Btu per pound of fluid. = loss of head, inches of water. fa = loss of head, feet of fluid. /it = total head, feet of fluid. hj, = differential pressure, inches of water. J -- mechanical equivalent of heat = 778 foot pounds per Btu. K = flow coefficient (correction factor), including velocity of approach correc tion factor, for flow through orifice, nozzle or Venturi. k = ratio of specific heat at constant pressure to specific heat at constant vol ume. L = perpendicular distance from axis of pipe, feet. 1 -- length of pipe, feet. M = Mach number. Niu = Reynolds number. P = correction factor for expansion of orifice plate with temperature, p = pressure, pounds per square foot. = stagnation pressure, po = critical pressure. Pb -- standard pressure to which correction is to be made, pounds per square inch, absolute. Pf = pressure of gas flowing, pounds per square inch, absolute. Qb = rate of flow, cubic feet per hour under standard conditions of pressure and temperature. Fluid Flow 99 Q. = rate of flow, cubic feet per hour. 0 = discharge rate, cubic feet per second. 0 = rate of flow, gallons per hour. q = heat transferred to the fluid per pound of fluid flowing. r gas constant. Rs = hydraulic radius = ratio of area of cross-section to wetted perimeter, r = radius of pipe in feet. s = entropy of fluid in Btu per (pound) (Fahrenheit degree). T = temperature, Fahrenheit degrees, absolute. yb = standard temperature to which correction is to be made, Fahrenheit de grees absolute. Tt = temperature of gas flowing, Fahrenheit degrees, absolute. u = internal energy, Btu per pound of fluid. y = velocity, feet per second. V -- critical velocity, feet per second. yJ -- velocity of sound, feet per second. ym = velocity, feet per minute. v = specific volume, cubic feet per pound. jy -- mechanical work, foot pounds per pound of fluid flowing. w = weight of gas flowing, pounds per second, u* = weight of gas flowing, pounds per hour. Y = expansion factor--correcting for expansion of gas under reduced down stream pressure. z -- elevation above some arbitrary datum, feet. REFERENCES 1 Friction Factors for Pipe Flow, by Lewis F. Moody (A .S.MJZ. Transactions, 66, 1944, 671-678; Discussion, idem. 66, 1944, 678-684); also, An Approximate Formula for Pipe Friction Factors (Mechanical Engineering, 69, 1947, 1005-1006). * History of Orifice Meters and the Calibration, Construction, and Operation of Orifices for Metering. Report of the Joint A.G.A.--A.S.M.E. Committee on Orifice Coefficients (American Society of Mechanical Engineers, 1935). * Gas Measurement Committee Report No. 2, Natural Gas Department (Amer ican Gas Association, 1935). * Thermodynamic Properties of Steam, by Joseph H. Keenan and Frederick G. Keyes (John Wiley & Sons, Inc., 1936). 6 Discharge Coefficients of Long Radius Flow Nozzles When Used with Pipe'Wall Pressure Taps, by H. S. Bean, S. R. Beitler, and R. E. Sprenkle (A.S.M.E. Transac tions, 68, 1941, 439-A42; Discussion, idem. 63, 1941, 442-445). 8 The Flow Mechanism and Performance of the Rotameter, by E. M. Schoenborn, Jr. and A. P. Colburn (Institute of Chemical Engineers, Transactions, 35, 1939, 359- 381). BIBLIOGRAPHY [AJ Principles of Thermodynamics, by G. A. Goodenough (Henry Holt & Co.). [B] Principles of Engineering Thermodynamics, by Paul J. Kiefer and Milton C. Stuart (John Wiley & Sons, Inc., 1944). [C] Fluid Mechanics, by Russell A. Dodge and Milton J. Thompson (McGrawHill Book Co., 1937). [D] Fluid Mechanics, by R. C. Binder (Prentice-Hall, Inc., 1943). (EJ The Physics of Solids and Fluids, by P. P. Ewald, H. Poschl and L. Prandtl (Blackie, 1936). [F] A Study of the Data on the Flow of Fluids in Pipes, by Emory Kemler, Hy draulic Paper HYD-55-2 (A.S.M.E. Transactions 55, No. 10, 7-22, 1933; Discussion, idem., 55, No. 10, 23-32,1933). [GJ The Flow of Fluids in Closed Conduits, by R. J. S. Pigott (Mechanical Engi neering 55, 1933, 497-501, 515). (H) Fluid Meters, Their Theory and Application (American Society of Mechanical Engineers, 4th edition, 1937).