Problem

What should I enter for the "Discharge Coefficient (fully open)" for a surge anticipator valve?

How can I calculate the discharge coefficient (Cv) of a SAV?

Solution

This would typically be obtained from the Surge Anticipator Valve manufacturer. If they don't provide it, you can calculate it based on the information that you do have.

For example, for a 4 inch opening (area of 0.087266 ft^2) and assuming an orifice coefficient of 0.6. Here is the orifice equation re-written as:

H = (Q/CA)^2/(2g)

Let's pick a flow of 1.0 cfs, which results in a pressure head (H) of (1.0 / (0.6 * 0.087266))^2 / (64.34) = 5.67 ft.

The following equation can be used to find the discharge coefficient:

Cv = ((39.693 * d^4) / ( H / (V^2 / 2g)))^0.5.

You can plug in the pressure head along with the same flow and corresponding velocity (using Q=VA) to derive the discharge coefficient:

Cv = ((39.693 * (0.33333)^4) / (5.67 / (11.456^2 / 64.34)))^0.5 =
0.41985 cfs/(ft H2O)^0.5

See Also

Modeling Reference - Surge Valves