Document 8Rpw5nwX4gpb3dJQqGJgbJDqd

86- CHAPTER 4 1949 Guide per Hour, and converting area in square feet to diameter in. inches, gives Qt = 3600 K 4X 144 V2gkt or where .. Q, = 19.635 KDf V2ght .. . (52) Qt = rate of flow in cubic feet per hour. i Di -- the diameter of the orifice or nozzle throat in inches. K = flow coefficient including correction for velocity of approach. Equation 52 is a general equation, expressing the flow of any fluid through an orifice or nozzle. Further use of it will be made as other types of flow are discussed. The differential loss, ht, is in. terms of feet of the fluid flowing through the orifice or nozzle. In the case of a gas flowing, where it is customary to read the differential pressure in inches of water, feet of gas must be converted to inches of water. Since dry air at 32 F and 14.7 psi absolute pressure weighs 0.0807 lb per cu ft, the weight of a cubic foot of any other: kind of gas under the same conditions is 0.0807 G, where G is the specific gravity of the gas referred to air. Water weighs 62.37 lb per cu ft at 60 F. Using also the relation of .12 in. in I ft, hw 62.37 _ 12 X 0.0807(7 in which hw is the differential pressure in inches of water. Also, since the gas flowing is not necessarily at 32 F and 14.7 psi, it is necessary to apply Charles' and Boyle's laws to.the density of the gas and therefore ,h 62,37 14.7 Tt 12 X 0.0807G X "pT`X 492 . (54) in which P; and Tt are the absolute pressure and temperature of the flowing gas. Substituting this in Equation 52, and combining the con stants, Qt = 218.44KDf (55) Then, to correct the value of Qt to any other standard conditions of pressure Pt, and temperature Th , using the gas laws, (56)' Equation 55 becomes , /^Tb Qt = 218.44KDf a y TiG (57) Finally, since gases expand under the conditions of reduced pressure downstream from the orifice.or nozzle, an expansion factor, Y, must.be added. The final formula, then, is Fluid Flow; ^. m Qt, = 218.44 KYDf /PiK. A ' T,G i 87 (58) In Equation 58, all the data must be observed at the time of measure ment except K and Y. These must be obtained from charts, fables, or formulas, derived from or based on the results of a great many experi ments, the results of which have been collected by a joint committee of i `----- - Gna Association and the American Society of Mechanical Fig. 7- Flow Coefficients, K, fob Square-edged Orifice Plates and Flange Taps in Smooth Pipe Note: From Table 6, Bibliography [H]. Fig. 8. Flow Coefficients, K, fob Square-edged Orifice Plates and , Radius Taps in Smooth Pipe Note: From Fig. 36d, Bibliography [K]. Engineers2-*. . The report of the two associations gives orifice coefficients as a function of the. Reynolds number and of the' ratio of orifice to pipe diameter, for pipes 2 to 12 in. and 14 in. in diameter, and for four different types of pressure taps in use in the United States. The coeffi cients are higher for the smaller pipe sizes. This is an effect of the turbu lence produced by the roughness of the pipe surface, a given roughness being relatively, greater with a small pipe than with a large one. Space does not permit presenting all the coefficient data that are avail able. However, if the pipe is smooth, drawn tubing, the effect of roughness is negligible, and the coefficients for the largest size of pipe apply also to smaller pipes. Figs. 7, 8, and 9 show these coefficients, iVRe, being the