Velocity-head loss across the valve

The concept of a velocity head has its roots in the theory of incompressible flow travelling along a pipe of uniform cross-section, so that the velocity is constant. However, its use has been extended to the characterization of bends, fittings and valves, where the cross-section varies, and also to compressible, i.e. gas, flow, where there is an implicit assumption of an average specific volume. 

The expression relating pressure drop, Ap (Pa), to the dimensionless velocity-head loss across the valve, K, may be written (cf. equation (4.48)) as 

A rearrangement of equation (7.3) for valve pressure drop and flow gives  

Hence by comparing (7.35) with (7.33), it is clear that the valve velocity-head drop, K,., is given by 

We may note that the pipe diameter and the valve diameter are by no means always the same indeed the requirement for good control often necessitates a valve size only 50% of the line diameter. Accordingly it is sensible to include a factor to make explicit allowance for this. At the same time, we may relate the velocity-head drop to the velocity-head drop at full-open by using equation (7.25), namely C = yCv Hence equation (7.36) may be rewritten  

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