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

[fonz]

TL;DR Summary

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

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

 

[Dullard]

The traditional way to do this is graphically. You have a pump curve from the manufacturer and can plot a 'system curve' for your valve (at any single fixed Cv). Where they intersect is your operating point. It is possible to 'calculate' the intersection, but you'll need to come up with a function to describe the pump curve. Don't forget any other significant (plumbing, filters, etc) losses in your system curve.

 

[fonz]

Thanks for the reply that is very helpful. On most system curves I have seen the friction factor is used or K factor for fittings etc. Do I just add the head loss due to Cv directly from the flow rate equation for a valve or do I need to convert to a K factor first?

 

[Dullard]

If I understand your question:
You need to create a 'pressure vs flow' curve for every system component that you want to consider. The 'net' system curve is the sum of those component curves. If you have Cv, use that to produce the curve; If you have K factor, use that - either will give you pressure as a function of flow.