Calculating Resistance Coefficient K from Cv or Kv

by Engineered Software, Inc.

For control valves, the valve capacity and flow characteristics are typically expressed in terms of a valve flow coefficient (Cv).  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 Cv 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 Kv represents the flow of water in m³/hr which can be passed by a valve with a pressure differential of 1 bar.

Kv is related to Cv by the following equation:

K_v = (0.865)C_v

The resistance coefficient (K) that is calculated or entered by the user on PIPE-FLO®'s valve/fitting screen is

K = f\frac{L}{D}

     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 Cv using the following equation:

K = \frac{890.9d^4}{C_v^2}

     Where, 
     d = inside diameter in inches

Or, using the coefficient Kv:

K = \frac{890.9d^4}{\bigg(\frac{K_v}{0.865}\bigg)^2}

If you know the Cv 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 Cv 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.