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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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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
H2H1=(D2D1)2\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}
Where
  • H1H_1= Head at diameter 1
  • D1D_1= Impeller diameter 1
  • H2H_2= Head at diameter 2
  • D2D_2= Impeller diameter 2
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