Calculating Resistance Coefficient K from C_{v} or K_{v}
by Engineered Software, Inc.
For control valves, the valve capacity and flow characteristics are typically expressed in terms of a valve flow coefficient (C_{v}). This article discusses how this flow coefficient can be used to calculate the equivalent resistance coefficient, or K value, used in the Darcy Weisbach equation.
The flow coefficient C_{v} is defined as the flow rate of 60°F water (in gpm) which can be passed by a valve with a pressure differential of 1 psid.
Similarly, the flow coefficient K_{v} represents the flow of water in m³/hr which can be passed by a valve with a pressure differential of 1 bar.
K_{v} is related to C_{v} by the following equation:
The resistance coefficient (K) that is calculated or entered by the user on PIPEFLO^{®}'s valve/fitting screen is
Where,
f = Darcy friction factor
\frac{L}{D} = equivalent length of a resistance to flow, in pipe diameters.
K can be calculated from the valve coefficient C_{v} using the following equation:

K = \frac{890.9d^4}{C_v^2} 
Where,
d = inside diameter in inches
Or, using the coefficient K_{v}:

K = \frac{890.9d^4}{\bigg(\frac{K_v}{0.865}\bigg)^2} 
If you know the C_{v} flow coefficient for a valve, you can either calculate a K value using the equation above, or you can use the dP Calculator feature to quickly determine the corresponding K value.
To use the dP Calculator feature, simply specify the C_{v} value for the flow rate (in gpm) and a pressure drop of 1 psi in the dP Calculator. The program calculates the corresponding K value.