Predict a centrifugal pump's new flow, head and absorbed power after a speed change or impeller trim, using the affinity laws Q ∝ r, H ∝ r², P ∝ r³.
Indicative. Verify against the manufacturer's pump curve.
For design guidance only. Always verify against the manufacturer's pump curve.
About this pump affinity laws calculator
This free pump affinity laws calculator predicts how a centrifugal pump's flow, total head and absorbed power change when you alter its speed (a variable-speed drive at a fixed impeller) or trim its impeller (at a fixed speed). Give it one known duty point, flow, head and shaft power, plus the two speeds or the two impeller diameters, and it returns the new duty point and the percentage change in each quantity. It is built for building-services and mechanical engineers sizing pumps, assessing VSD energy savings or checking the effect of an impeller cut. Everything runs in your browser. Nothing is uploaded.
How the affinity laws are calculated
The pump affinity (or similarity) laws relate the new duty point to the original through a single drive ratio r. For a speed change r = N₂/N₁; for an impeller trim r = D₂/D₁. Flow scales linearly, head with the square and power with the cube of that ratio: Q₂ = Q₁·r, H₂ = H₁·r² and P₂ = P₁·r³. The cube law on power is why even a modest speed reduction yields a large energy saving, running a pump at 80% speed needs only about half the power. The exponents 1, 2 and 3 follow the Hydraulic Institute (ANSI/HI) pump standards and Karassik's Pump Handbook; the power law assumes pump efficiency stays roughly constant between the two conditions.
Frequently asked questions
When should I use speed vs impeller diameter?
Use the speed ratio for a variable-speed drive or a motor with a different rated speed at a fixed impeller. Use the diameter ratio when an impeller is physically trimmed at constant speed. The diameter result is advisory: accuracy falls off beyond roughly 10–20% trim because impeller efficiency shifts with diameter, so verify against the manufacturer's trimmed-impeller curve.
Why does power scale with the cube of the ratio?
Hydraulic power is the product of flow and head. Flow scales with r and head with r², so their product, and therefore the absorbed power. Scales with r³. This cube relationship is the basis of the large energy savings achievable by reducing pump speed rather than throttling a valve.
Are the affinity laws exact?
They are an idealised model that assumes constant efficiency and geometric similarity. They are very accurate for speed changes over a wide range, and a good first estimate for small impeller trims. For final selection always confirm the predicted duty point sits on the manufacturer's published pump curve.