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Pump Affinity Law: Head vs Impeller Diameter

H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}
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Worked example: 320 mm impeller makes 40 m; 25 m needs a 252.98 mm trim. Press Try an example to run it live, then adjust anything.

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Pump Water HorsepowerPump Brake HorsepowerPump Affinity Law: Head vs SpeedPump Specific Speed (Ns)

See also

Pump Affinity Law: Flow vs Impeller Diameter: Both use impeller diameter.Pump Affinity Law: Head vs Speed: Both use pump total head.Pump Brake Horsepower: Both use pump total head.Pump Specific Speed (Ns): Both use pump total head.Pump Water Horsepower: Both use pump total head.Total Dynamic Head: Both use pump total head.
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Pump Affinity Law: Head vs Impeller Diameter explained

D1D2H1H2

Head comes from impeller tip speed, and tip speed at fixed rpm is proportional to diameter, so head follows diameter squared. A 12 in impeller making 150 ft, trimmed to 10.8 in, drops to 150 × 0.9² = 121.5 ft. Run the relation backwards to size a trim: to bring 40 m of head down to 25 m on a 320 mm impeller you need 320 × √(25/40) ≈ 253 mm, and any competent shop will machine it to the nearest millimetre.

Because power is head × flow, the diameter laws also imply power ∝ D³: the same cube that governs speed. But unlike a speed change, trimming is permanent, so most engineers cut conservatively (aim high, test, trim again) rather than machining straight to the calculated diameter on the first pass.

Pump Affinity Law: Head vs Impeller Diameter formula

H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}
Where
  • H1H_1= Head at diameter 1 (m)
  • D1D_1= Impeller diameter 1 (mm)
  • H2H_2= Head at diameter 2 (m)
  • D2D_2= Impeller diameter 2 (mm)
Revised 16 October 2026
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formula.expert. (2026, October 16). Pump Affinity Law: Head vs Impeller Diameter Calculator. https://formula.expert/solvers/pump-affinity-head-diameter

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