Document ev0OQNOJjQ7JBKjzbe0L1wE9m

80 CHAPTER 4 1954 Guide 8, respectively. Additional specifications are given in References 2, 3, and 4 at end of chapter. The measurement of flow in head meters is dependent upon observations of a static pressure difference between two parts of the system. In gen eral, there exists a reduction in area, either by a smooth contour as in the case of a Venturi or flow nozzle, or by a vena contracta following an orifice. -In either case, the flow will be given by a suitable modification of Equa tions 47 and 48. Adding a correction term, these become AjC w V 2ffpAp Vl - ? (49) Fluid Flow 81 and Q = KAi V2ffAf (53) The coefficients K and C will be determined by the area ratio A1/A1, or by the diameter ratio Di/Dt and the Reynolds number. Extensive data are available from various sources.1, * Figs. 9, 10,11, 12 show repre sentative values of K based on Ns,, the Reynolds number, and the ratio of diameter of the orifice or nozzle throat to pipe diameter. In any specific application, numerical values for areas, densities, and pressure units can be substituted in Equations 52 and 53 to obtain compact working formulas. In cases where the tests are run under non-standard Fig. 12. Flow Coefficient fob International Standards Association Flow Nozzle as a Function of Abea Ratio (Di/Di)! and the Reynolds Number Nk. Note: From Reference 3. Used by permission of ASME and AjC ,____ Q = V2sA' (so) In all cases, A2 refers to the minimum area of the Venturi, nozzle, or orifice. The correction factor C is introduced to account for any loss due to departure from isentropic flow, and for any deviation between the downstream measured pressure and the actual pressure at the minimum section. Since these corrections are usually dependent on configuration, as described by the ratio of upstream to minimum area A1/A2, it is often convenient to introduce a combined flow coefficient, K which is C K = V1-0* (51) so that w = KA,\/2gp&p (62) Fig. 13. Relation of Expansion Factor, <j>, fob Nozzles to Diameter Ratio and Pressure Loss for Air and Other Diatomic Gases conditions, care must be taken that proper adjustment be made in com puting flow rates. In measuring the flow of compressible, fluids, the approximate Equations 52 and 53 must be corrected for density variations. The need for such correction is evident by comparing Equations 35 and 38 with Equation 47. Introducing a multiplicative correction factor 0 the equation for flow with no loss becomes: A%ft = vT-> \/2gn(p, - p,) By comparison with Equation 35, (54) <t> From Equations 34 and 35, k Vt 1 -- y) 2 Pi (p./pi) - 1 A/iVAfP = 0,(P./Pi),,k (55) (56)