Choked Flow in Control Valve Applications ~ Learning Instrumentation And Control Engineering Learning Instrumentation And Control Engineering

### Choked Flow in Control Valve Applications

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Choked flow is also known as critical flow in control valve applications. It occurs when an increase in pressure drop across the valve no longer creates an increase in flow.  In liquid applications, the capacity of the control valve is severely limited if the pressure conditions for the liquid are low enough to cause flashing and cavitation.

For gases and vapours, the capacity is limited if the velocity reaches the sonic velocity (as referred to as MACH 1). To understand how these conditions occur, we look at the normal pressure to flow relationship for a control valve and see when choked or critical flow conditions occur. The basic relationship between flow and pressure in a control valve is given by:

$Q = C_v\sqrt{\frac{ΔP}{SG}}$

Where:
Cv = The flow coefficient of the control valve.
ΔP = is the pressure drop across the control valve
SG = Specific gravity of fluid referenced to water at 60 degree Fahrenheit
Q  = Flow in US gallons per minute

The graph below illustrates the relationship between flow Q and ΔP and also when choked flow sets in for a liquid when vapour formation occurs at the vena contracta point within the valve:

As seen from the graph as the pressure differential (ΔP) across the valve increases, the flow will reach a choked flow condition where no further flow increase can be obtained with increasing ΔP . Vapour formation in liquid flow is generally termed flashing (see how flashing takes place in a control valve) and it results in a vapour stream or bubbles continuing downstream from the valve. If the bubbles condensed again, the transient effect is described as cavitation (See how cavitation takes place in a control valve)
Volumetric and Mass Flow through Control valve in Liquid Service
As already explained above, choked flow is a limiting flow rate. With liquid streams, choking occurs as a result of vaporization of the liquid when the pressure within the valve falls below the vapour pressure of the liquid.
Under normal flow conditions, both volumetric and mass flow through a control valve are given by: