Document gwKaERn4BZzK9wEYLGxorZBQ

88 CHAPTER 4 1946' Guide the static pressure is at a minimum. Its location, and the location of ' the downstream vena contracts tap, varies with the ratio of orifice to pipe diameter, and with /ate of flow, as shown in Fig. 12; the tap is generally located<in accordance with the mean curve in the figure. Expansion Factor ior Gases The expansion factor, F, for gases (for liquids, Y =;1) is found from the empirical formula Y = 1 -- (0.41 + 0.35ft4) (^' ~ (55) This is applicable to flange, radius, and vena contracta taps. For pipe . taps, the formula is Y = 1 -- [ 0.333 + 1.145 (P* + 0.7^ + 12g`) J j> ~ pl/k^ (56) Values of F for air, computed from these equations, are given in Fig. 13 and Fig. 14. Computing Orifice Discharge With this information it is possible to compute the discharge from an orifice if the Reynolds number is known. Here an odd complication is . encountered--when the value of NRc is computed, the rate of flow, which is the unknown quantity, must be used in the computation. How ever, it will be noted in Figs. 7, 8, 9, and 10 that the orifice coefficient does not change greatly as NRc changes. If, then, an estimate is made of the velocity, using this in computing NRe, and if the corresponding coef ficient is used in Equation 54, a value for the rate of flow will be found. Using this velocity to compute a corrected value of NRe and repeating the process, a more nearly correct value of Qt is found. This cut-and-try method may be continued for several more cycles, but generally the first or second correction will be found sufficient. . Another method, would be to use the value of AT, corresponding to NRe = 00 , modifying this with a factor involving the rate of flow, deter? mined from the temperature, and the differential and static pressures. This method is used by the American Gas Association3.. STEAM FLOW MEASUREMENT While steam may be considered as a gas, its measurement differs from that of the usual gases because of a number of factors. Equation 48 serves as the starting point.1 Since it is usual to measure the differential pressure in inches of wafer, it is necessary -to convert fe, the head in feet in terms of the flowing fluid, to few, the actual head in inches of water, using the equation' ' ;' f' ' .(57) where ' Pw = the density of.water at 60 F (62.37 lb per cubic foot).. P = the density of the flowing fluid. Substituting Equation 57 in Equation 48 gives 1 . > Fig. 13. Expansion Factor for Air and Other Diatomic Gases Applicable to Flange, Radios and Vena Con tracta Taps 89 Fig. 12. Location of Vena Contracta in Relation to Ratio of Orifice to Pipe Di ameter and to Rate of Flow