Pressure distribution through the valve

We may appeal to the energy equation for general, steady-state flow to gain an insight into the variation in pressure through the valve  

Assuming for simplicity that the valve is horizontal, we may derive from (4.15) an expression for the change in pressure along the valve, dp  

The change in pressure thus depends on two terms, which may be additive or in opposition. Since the eneigy lost to friction, /F, must always be positive, the effect of the first term will be to reduce pressure in the direction of flow. However, the sign of the second term depends on whether the flow velocity is increasing or decreasing. 

The argument above demonstrates that the velocity of both liquids and gases will increase as far as the valve s throat and decrease thereafter. Accordingly, the second 

It is found for practical valve designs that there is always a rise in pressure over the outlet section for liquids, so that the throat pressure, p will be less than the outlet pressure, p2.  

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