The Valve Flow Coefficient (Cv) ~ Learning Instrumentation And Control Engineering Learning Instrumentation And Control Engineering

The Valve Flow Coefficient (Cv)

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The valve flow coefficient Cv or its metric equivalent Kv has been adopted universally as a comparative value for measuring the capacity of control valves. 
The valve flow coefficient, Cv, is the number of U.S. gallons per minute of water at 60°F that will flow through a control valve at a specified opening when a pressure differential of 1psi is applied across the valve:
The metric equivalent of Cv is Kv, which is defined as the amount of water that will flow in m3/hr with 1bar pressure drop. Converting between
the two coefficients is based on this relationship:
$C_v = 1.16K_v$

For a liquid, the flow rate provided by any particular Cv is given by the basic sizing equation:
$Q = C_v\sqrt{\frac{ΔP}{SG}}$ 

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.

Hence a valve with a specified opening giving Cv = 1 will pass 1US gallon of water (at 60 degree Fahrenheit) per minute if 1psi pressure difference exists between the upstream and down stream points on each side of the valve. For the same pressure conditions if we increase the opening of the valve to create a Cv = 20, it will pass 20 US gallons per minute provided that ΔP across the valve remains at 1psi.

$Q = {\frac{1}{1.16}}C_v\sqrt{\frac{ΔP}{SG}}$

Where:
Q is in m3/hr , ΔP is in bars and SG = 1 for water at 15degree Celsius

In metric units, the same valve above with a specified opening giving Cv = 1 will pass 0.862m3/hr of water (at 15 degree Celsius) if 1bar pressure difference(ΔP) exist between upstream and downstream points on each side of the valve.
These simplified equations give us an understanding of the underlying principles of valve sizing. If we know the pressure conditions and the SG of the fluid and we have the Cv of the valve at the chosen opening, we can predict with some measure of certainty the amount of flow that will pass.

It must be noted that it is not that simple to predict the amount of fluid passing through a control valve as there are many factors which will modify the Cv values
for the valve and there are also limits to the flow velocities and pressure drops that a valve can handle before we reach critical or choked flow beyond which we cannot increase flow through the valve further. Manufacturers of valves typically have tabulated Cv values for various opening or travel of a given valve. 

These Cv values are used in valve sizing. Masoneilan and Fisher are two recognized manufacturers of various types of valves. They have their commercial software for the valve sizing process which usually has a rich data base for Cv values for all the types of valves they produce.