Free Online Pump Affinity Laws Calculator

The affinity laws predict how a centrifugal pump's flow, head and power change when its speed or impeller diameter changes. This calculator applies them to find the new duty point and the power saving from slowing a pump with a variable-speed drive, per the Hydraulic Institute / IS 9137.

The laws are simple but powerful: flow scales with speed, head with speed squared, and power with speed cubed. That cube relationship is why variable-speed pumping saves so much - a 20% speed reduction roughly halves the power. Trimming the impeller has the same effect for a fixed-speed pump, though only over a limited range before efficiency falls.

Example: A pump delivering 50 L/s at 30 m and 22 kW is slowed to 80% speed. New flow = 50 × 0.8 = 40 L/s, new head = 30 × 0.8² = 19.2 m, new power = 22 × 0.8³ = 11.3 kW - a 49% power saving for a 20% speed cut. This is the core benefit of variable-speed pumping on variable-flow systems.

How each quantity scales with speed (or impeller diameter) ratio:

Practical Notes

The affinity laws are exact for speed change and a good approximation for modest impeller trims (usually within about 20% of diameter before efficiency drops). They assume the system curve passes through the origin (mostly friction). Where a system has significant static head, the operating point shifts along the real system curve, so the savings are a little less than the ideal cube law - but still large. This is why VFDs pay back quickly on variable-flow pumping.

Ideal relations - real savings depend on the system curve and motor/drive efficiency.