# How to calculate a pump's operating point for a fully open control valve

## Summary:

How to calculate the flow rate and pressure of a centrifugal pump through a fully open valve.

## Main Question or Discussion Point

How do you calculate the flow rate and differential pressure (the operating point on the pump curve) for a centrifugal pump if all of the flow is through a single control valve with known $C_V$, discharging to atmosphere?

Clearly the flow rate and differential pressure of the pump will be some point on the pump curve to match the flow and pressure drop across the valve. As the $C_V$ increases, that point will move further down the curve i.e. more flow at less pressure drop. It is easy enough to calculate the flow rate through a valve for a known pressure drop and $C_V$, but if only the $C_V$ is known I struggle to work this out.

Thanks