Pump Affinity Law Calculator

Pump retrofitting: calculating new flow when replacing a motor with different speed.

Multi-speed pump applications: determining flow at each speed setting.

Energy savings estimation: reducing speed saves energy per the affinity laws.

In variable-speed pumping applications (VFD-controlled centrifugal pumps), the affinity laws are the primary engineering tool for estimating the energy savings from speed reduction.

A pump running at 75% of design speed delivers about 75% of design flow at 56% of design head (0.75²) and consumes about 42% of design power (0.75³) — the 58% energy reduction from a 25% speed reduction is the basis of the VFD retrofit business case, with typical payback periods of 1–3 years for constant-torque loads like centrifugal fans and pumps.

The US DOE Industrial Assessment Centers (IAC) and the Hydraulic Institute's variable-speed pumping guide both use the affinity laws as the primary calculation method for VFD retrofit economic analysis.

Pump impeller trimming (a common retrofit to match a pump to a lower-flow system) follows a different relationship than the affinity laws — the trimmed impeller laws (also called the 'laws of similitude' for impeller diameter) are Q ∝ D, H ∝ D², P ∝ D³, with D being the trimmed impeller diameter.

A 90% impeller trim (cutting the impeller to 90% of its original diameter) reduces the flow to 90% of design, the head to 81% of design, and the power to 73% of design.

Multi-speed pump applications (Paharpur cooling tower fans, industrial process pumps with two-speed motors) use the affinity laws to compute the performance at each speed setting, with the energy savings at low speed significant for cycling loads.

Pump performance verification at site (per Hydraulic Institute 14.6 acceptance testing) uses the affinity laws to convert the field-measured performance at one speed to the equivalent performance at the rated speed, allowing comparison to the manufacturer's published curve.

Pump selection for variable-speed applications per the HI 9.6.7 and the US DOE pumping system assessment guide requires the consideration of the affinity law relationships to size the pump correctly for the operating range — a pump sized for the design point at 100% speed will not deliver the same proportional head at 50% speed (it delivers 25% of design head, which may be insufficient for the system at low flow).