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Pump Affinity Laws Calculator

Scale flow, head and power for a centrifugal pump speed change or impeller trim — Q∝r, H∝r², P∝r³

⚖️ Pump Affinity Laws
Enter a known performance point, then change either the speed (impeller fixed) or the impeller diameter (speed fixed). The calculator scales flow, head and power by the affinity laws: Q ∝ r, H ∝ r², P ∝ r³. Efficiency is assumed constant between the two points.

Mode & Reference Point

GPM
ft
bhp
Leave blank to skip the power scaling.
ft
Scaled ≈ r² for a speed change only (approximate).

Speed Change

rpm
rpm
Ratio r = N2 / N1. A VFD makes this exact at the same impeller.

Impeller Trim

in
in
Ratio r = D2 / D1. Keep trim within ~10–15% of D1.

What This Calculates

Affinity Ratio (r):
r = N2/N1 for a speed change, or r = D2/D1 for an impeller trim.
Scaled Flow & Head:
Q2 = Q1·r and H2 = H1·r² — flow scales linearly, head with the square.
Scaled Power:
P2 = P1·r³ — the cube law; halving speed cuts power to one-eighth.
NPSHr & Trim Limit:
NPSHr2 ≈ NPSHr1·r² (speed mode, approximate); a warning flags impeller trims beyond ~10–15% where the laws lose accuracy.

📘 The Affinity Laws

For a geometrically similar centrifugal pump at constant efficiency, with ratio r:

Q₂ / Q₁ = r    (flow ∝ ratio)
H₂ / H₁ = r²   (head ∝ ratio²)
P₂ / P₁ = r³   (power ∝ ratio³)
Speed change (impeller fixed)
  • r = N₂ / N₁
  • NPSHr₂ ≈ NPSHr₁ · r² (approximate)
Impeller trim (speed fixed)
  • r = D₂ / D₁
  • Keep the trim within ~10–15% of D₁

When They Apply & Limitations

The affinity laws are an idealization. Keep these limits in mind:

  • Constant efficiency is assumed — true only for modest changes; large trims and big speed drops shift the best-efficiency point.
  • Speed changes are nearly exact because the impeller geometry is unchanged (the ideal use case for a VFD).
  • Impeller trims drift beyond ~10–15%: the flow no longer fully fills the casing, so actual head falls below the r² prediction.
  • NPSHr scaling (r²) applies to a speed change only and is approximate; trimming the OD does not change the inlet eye, so NPSHr stays roughly constant.
  • Always confirm a re-rate against the manufacturer's published performance / trim curve.

Standards Reference

  • Affinity laws: Pump similitude — Q∝r, H∝r², P∝r³
  • ANSI/HI 1.3: Hydraulic Institute — centrifugal pump design & application
  • API 610: Performance curves & rated point definition
  • Trim guideline: Keep impeller trim within ~10–15% of original diameter

Frequently Asked Questions

What are the pump affinity laws?

The affinity laws scale a centrifugal pump's performance when speed or impeller diameter changes. Flow varies directly with the ratio (Q2/Q1 = r), head varies with the square (H2/H1 = r²), and power varies with the cube (P2/P1 = r³). For a speed change r = N2/N1 with the impeller fixed; for an impeller trim r = D2/D1 with the speed fixed. Efficiency is assumed constant between the two points.

How much can you trim a centrifugal pump impeller?

As a practical rule, keep an impeller trim within about 10–15% of the original diameter (r between roughly 0.85 and 1.0). Within that band the affinity laws predict head and flow well. Beyond ~15% the flow leaving the trimmed impeller no longer fully fills the casing, efficiency drops, and the actual head tends to fall below the affinity prediction — confirm any large trim against the manufacturer's published trim curve.

Should I use a VFD or trim the impeller to reduce pump output?

A variable-frequency drive (VFD) changes speed without machining, makes the speed-affinity laws essentially exact, is reversible, and saves the most energy because power drops with the cube of speed. Trimming the impeller is a permanent, lower-cost fix when no VFD is available, but it is limited to ~10–15% and slightly reduces peak efficiency. Use a VFD for variable duty or when future re-rates are likely; trim for a fixed, modest over-performance correction.