Pump Affinity Laws Calculator

For a fixed pump geometry with only speed changing, the similarity laws are Q ∝ N, H ∝ N², P ∝ N³. For a modest impeller trim in the same casing, the commonly used screening approximation applies the analogous ratios Q₂/Q₁ ≈ D₂/D₁, H₂/H₁ ≈ (D₂/D₁)², and P₂/P₁ ≈ (D₂/D₁)³. The diameter relations are less exact because trimming does not geometrically scale the whole pump.

Power is the product of flow and head (roughly, ignoring efficiency changes): P ∝ Q·H ∝ N·N² = N³. This is exactly why a seemingly modest 20% speed increase results in a much larger 73% power increase (1.2³=1.728) — and why running a pump faster than needed is an expensive way to get a bit more flow, while a variable-speed drive that trims speed down to match actual demand can save a disproportionate amount of energy.

A variable-speed drive changes N continuously and reversibly — the pump can run at any speed within its motor and mechanical limits, and the affinity laws apply accurately across a fairly wide speed range for a fixed pump geometry. An impeller trim is a one-time mechanical modification (machining material off the impeller) that permanently changes D; it's cheaper than buying a new pump when a pump is oversized for its duty, but the affinity laws become progressively less accurate for larger trims (typically beyond about 10–15% diameter reduction), since trimming changes the impeller's actual blade geometry, not just its scale.

The affinity laws scale a single known operating point to a new speed or diameter — they don't by themselves tell you where that pump will actually operate in a real system, which depends on the intersection with the system curve (see the Pump Operating Point and Pump System Curve tools). If you know the pump's full curve, applying the affinity laws to every point on it traces out the new curve at the new speed or diameter.

Because power scales with the cube of the speed ratio (P ∝ N³), not linearly — 1.2³ = 1.728, a 72.8% increase. This cubic relationship is exactly why variable-speed control is so effective for energy savings in variable-flow applications: running a pump at 80% speed instead of 100% for lower-demand periods cuts power to roughly 0.8³ ≈ 51% of full-speed power, far more than the 20% flow reduction alone would suggest.

Not reliably — the affinity laws assume the impeller's geometry scales proportionally, which holds reasonably well for small trims (roughly under 10–15%) but breaks down for larger ones, since a heavily trimmed impeller's blade angles and flow passages no longer resemble a simple scaled-down version of the original. For larger trims, use the pump manufacturer's actual trim curves rather than the affinity laws.

Not directly — the basic affinity laws assume efficiency stays constant between the original and new point, which is a reasonable approximation for modest speed changes but becomes less accurate for large speed changes or impeller trims, where efficiency can shift meaningfully. This is part of why the power law (P ∝ N³) is treated as approximate for large changes, even though the flow and head laws are quite robust.

Throttling a valve to reduce flow wastes energy as pressure drop across the valve — the pump still does the work of producing full head, then that energy is destroyed at the valve. Trimming the impeller (or better, using a VFD) actually reduces the pump's own power consumption to match the new lower duty point, rather than producing excess head and throwing it away.