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The flow rate of a given system is that where the two curves of pressure versus flow rate intersect (point 1 in Figure 16). When a control valve (or Control Valve Characterization Control valves are characterized by a discharge coefficient Cd . 9 for chamfered or rounded configurations. For gas flows at pressure ratios below the choking critical [Equation (24)], the mass rate of flow is Pd ( k – 1) ⁄ k  Pu  P · m = Cd Ao C 1  ----------- -------d- 1 –  ------  P u  Tu  Pu Fig. 14 Valve Action in Pipeline (36) where C1 = k R T u, d = = = = 2k ⁄ R ( k – 1 ) ratio of specific heats at constant pressure and volume gas constant absolute temperature subscripts referring to upstream and downstream positions Incompressible Flow in Systems Flow devices must be evaluated in terms of their interaction with other elements of the system, for example, the action of valves in modifying flow rate and in matching the flow-producing device (pump or blower) with the system loss.

Ed. 1938. Modern developments in fluid mechanics. Oxford University Press, London. Reprinted by Dover Publications, New York. R. E. Bullock. 1967. Centrifugal fan sound power level prediction. 1. Heskested, G. 1965. An edge suction effect. AIAA Journal 3:1958. Heskested, G. 1970. Further experiments with suction at a sudden enlargement. Journal of Basic Engineering, ASME Transactions 92D:437. F. 1965. Fluid dynamic drag, 3rd ed. Published by author, Midland Park, NJ. Hydraulic Institute. 1961.

2. Thus a pitot tube in air is influenced by compressibility at velocities over about 66 m/s. Flows through a converging conduit, as in a flow nozzle, venturi, or orifice meter, also may be considered isentropic. Velocity at the upstream station 1 is negligible. 4 for air and diatomic gases. The Bernoulli equation of steady flow, Equation (12), as an integral of the ideal-fluid equation of motion along a streamline, then becomes · m = V2 A2 ρ2 = p 2 ⁄ k p2 ( k + 1 ) ⁄ k 2k ----------- ( p 1 ρ 1 )  ----2- –  ----- k–1  p 1  p 1 A2 (21) The corresponding incompressible flow relation is ∫ 2 dp V ------ + ------ = constant 2 ρ (14) where, as in most compressible flow analyses, the elevation terms involving z are insignificant and are dropped.

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ASHRAE 2001 HVAC Fundamentals Handbook

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