Water hydraulics
Pump-speed affinity estimate
- where
- scaled flow (L/min)
- original flow (L/min)
- speed ratio
- scaled head (m)
- original head (m)
- scaled shaft power (W)
- original shaft power (W)
- new rotational speed (rpm)
- original rotational speed (rpm)
Explain this equation
Estimates how a centrifugal pump's flow, head and power change when its speed changes. Use it to estimate the effect of turning a variable-speed pump up or down.
r is the speed ratio, new speed n₂ over original speed n₁. q, h and P are flow, head and shaft power at each speed.
Flow scales with how fast the impeller turns, so it goes in proportion to r. Head depends on the velocity the impeller gives the water, squared, so it goes with r². Power is flow × head, so it goes with r³.
Sense check: dropping to 80% speed gives 80% flow, 64% head and about 51% power. That cube law is why slowing a pump saves so much energy.
Watch out: this assumes the same impeller and constant efficiency. The real operating point depends on where the pump curve meets the system curve.
Enter your values to see the result.
Good to know
Same impeller and similar operation, approximately constant efficiency. Actual system operating point must be found from system and pump curves.
Sources
Results are arithmetic only. Worked examples are not recommended design settings. This library does not provide automatic gas pipe selection, live gas tightness tests, purging procedures, combustion acceptance limits, installation approval or commissioning certification. Manufacturer data and the applicable current method remain essential.