I'm looking for a formula to arrive at a pump curve for a centrifugal pump: $H(Q, n)$ - total head delivered as a function of flow and speed (rpm), and of course some pump specific parameters. I find no formula I can transform into this. For actual pump selection I would of course use the pump curves from the supplier, but a formula like this would be interesting for simulation purposes of pumping systems where VFD is used.
As both head and flow are mostly a function of speed, impeller size and shape I think a non purely empirical fomrlua for a pump curve should exist.
p.s. Alternativly, I considered using a simple polynomial or similar curve and fitting it numerically to an existing pump curve. Pump simulators, is this an actually useful approach lacking an analytically correct curve?