This doesn't sound right.
Back Pressure is normally used to "hold back pressure", i.e. it is the pressure upstream of the valve which is the control point. Doing this on a bypass around a pump won't hold any pressure back. If you want to regulate the pressure coming out of the pump then this isn't a good way to do it.
what are you trying to do? Regulate pressure downstream of the pump? Or somewhere else?
What type of pump ~(positive displacement or centrifugal?)
Is flow always there?
Are the pressures (inlet and outlet constant?)
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