Pump & Fan Affinity Laws Calculator

How it works

Q₂ = Q₁ × (N₂/N₁); H₂ = H₁ × (N₂/N₁)²; P₂ = P₁ × (N₂/N₁)³ — the same ratios apply to impeller diameter D₂/D₁ at constant speed (approximately; head ∝ D^2–2.5 for trims)

For a centrifugal pump or fan, changing speed scales the whole performance curve predictably: flow with speed, head with speed squared and power with speed cubed. The same relationships hold approximately for trimming the impeller at constant speed, which is how a manufacturer tailors a stock pump to a duty. The laws make variable-speed control so attractive — 80% speed gives 80% flow for 51% power — and let you re-rate an existing machine for a new belt ratio or drive frequency. Their limit is that they move a point along a path of constant efficiency and assume the system follows a pure friction curve; where static head dominates, the actual new operating point must be found where the scaled pump curve meets the system curve, and efficiency drops as the pump moves off its best-efficiency region.

Worked example

A pump delivering 500 gpm at 120 ft and 22 hp at 1,750 rpm slowed to 1,450 rpm (ratio 0.829): 414 gpm at 82 ft for 12.5 hp — a 43% power saving. To hit exactly 400 gpm it would need 1,400 rpm (48 Hz); trimming the 10″ impeller to 9.25″ instead gives about 463 gpm at 103 ft.

Frequently asked questions