How to Size a Control Valve

Control valve sizing refers to the procedure determining the correct size of a valve body. A valve sizing equation for incompressible fluids is given by:

Which is the same as:

Where C_v is the valve flow coefficient/valve capacity

P₁ = Upstream fluid pressure

P₂ = Downstream fluid pressure

ρ = Mass density of fluid

Q = Volumetric fluid flow rate

∆P = The pressure drop across the valve

Alternatively the above equation is sometimes written as:

Where G is the specific gravity, C_v i.e. valve capacity (in US) is defined as the number of gallons per minute of water that will flow through a valve with 1 PSI of pressure drop. Elsewhere in the world, valve capacity is defined as the amount of cubic meters per hour of water that will flow through a valve with a pressure drop of 1 bar, symbolized as K_v.

The above equations can be written with the quantities in SI units:

Alternatively, it may be written as:

The last two forms of the equation derive from its original specification in terms of US gallons.

The table below shows typical values of A_v, C_v and valve size:

Table 1.0: Flow Coefficients and Valve Sizes

Example: Consider the problem of determining the size of a valve that is required to control the flow of water when the maximum flow required is 0.012 m³/s and the permissible pressure drop across the valve at this flow rate is 300 kPa.

Solution

Using this equation

Then, since the density of water is 1000 kg/m³,

Using table 1.0 above, the valve size is 960 mm.

The flow coefficient of a control valve C_v as indicated earlier is a numerical value expressing the number of gallons per minute flow of water the valve will pass with a constant pressure drop of 1 PSI from inlet to outlet. This rating is normally given for the valve in its wide open state. For instance, a control valve with a C_v rating of 50 should flow 50 gallons per minute of water through it with a 1 PSI pressure drop when wide open. The flow coefficient value for this same control valve will be less than 50 when the valve position is anything less than fully open. When the control valve is in the fully shut position, its C_v value will be zero. Therefore, C_v is variable not a constant for any control valve, though control valves are often specified simply by their maximum flow capacity. It is thus important that any control valve sized large enough (possess adequate maximum C_v capacity) to flow the greatest expected flow rate in any given process installation. If you select a valve that is too small for an application, it will not be able to pass adequate process fluid through it when required. When selecting a valve, it is important to consider the valve style, inherent characteristics and valve size that will offer the broadest possible range for the application.

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