Pump Affinity Laws Calculator
Predict how a centrifugal pump's flow, head and power change when you change its speed, using the pump affinity laws. Enter the original duty point and the old and new pump speeds and the tool scales flow with speed, head with speed squared and power with speed cubed.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the original flow Q₁ (L/s), original head H₁ (m) and original pump speed N₁ (rpm) at the known duty point.
- Enter the new pump speed N₂ (rpm) you want to run at — for example the reduced speed from a variable-speed drive.
- Optionally add the original absorbed power P₁ (kW) to also get the new power P₂, then read the new flow, head, power and the speed ratio.
How it works
For a fixed impeller and fluid, the affinity laws state that flow is proportional to speed (Q₂ = Q₁·N₂/N₁), head is proportional to the square of the speed ratio (H₂ = H₁·(N₂/N₁)²) and shaft power is proportional to the cube of the speed ratio (P₂ = P₁·(N₂/N₁)³). The tool computes the speed ratio N₂/N₁ once and applies these three scalings.
Worked example
Worked example. A pump delivering 20 L/s at 30 m absorbing 8 kW at 1450 rpm is sped up to 1740 rpm. The ratio is 1740/1450 = 1.2, so Q₂ = 20 × 1.2 = 24 L/s, H₂ = 30 × 1.2² = 43.2 m and P₂ = 8 × 1.2³ = 13.824 kW.
Common mistakes
- Using the affinity laws for a diameter (impeller trim) change with the same exponents — the head/power laws differ slightly when the diameter, not the speed, is varied.
- Assuming the new duty point lies exactly on the pump curve when the system has a large static lift — the affinity curve is a cube law through the origin, which only matches a friction-dominated system.
- Forgetting that efficiency is assumed constant; at very different speeds the efficiency and NPSH required also change.
Frequently asked questions
Why does halving the speed cut power to one eighth?
Power scales with the cube of the speed ratio, so at half speed P₂ = P₁ × 0.5³ = 0.125·P₁ — one eighth of the original power. This cube relationship is the reason variable-speed drives save so much pump energy.
Do the affinity laws work for impeller diameter changes?
Approximately, for small trims: flow scales with diameter and head with diameter squared, but power and efficiency behave a little differently than for a speed change, so for diameter changes rely on the manufacturer's trim curves.
Related tools
- Darcy-Weisbach Head Loss Calculator
- Friction Factor (Moody) Calculator
- Pump Power Calculator
- NPSH Available Calculator
- Manning Pipe Flow Calculator
- Nozzle Flow Calculator
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Tip: Enter any known values to calculate the remaining results.
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