How pump affinity laws work when you change speed
As long as the impeller stays the same, a centrifugal pump follows fixed ratios when its speed changes. These are the affinity laws: flow varies directly with speed (QāN), head varies with the square of speed (HāNĀ²) and brake horsepower varies with the cube of speed (PāNĀ³). Enter the existing duty point and the new speed to see where the pump lands.
That cube relationship is why variable frequency drives save so much energy. Drop the speed to 80% and flow falls to 80%, but power falls to 0.8Ā³, or 51.2% ā close to half the electricity for the same pump. Throttling a discharge valve gives no such saving, so speed control wins wherever flow is adjusted often.
The laws only hold over a narrow band where efficiency stays roughly constant. Once the speed ratio moves well outside 0.5 to 1.2, efficiency falls off and the predicted values drift. Real piping also has a static lift the pump must overcome, so measured flow at reduced speed is often lower than the calculation suggests. Low-speed running can also starve bearing cooling and fall under the pump's minimum flow, so confirm the final change with a mechanical engineer and the manufacturer's curves.
Frequently Asked Questions
Power follows the cube of speed, so at half speed the theoretical draw is one eighth. In practice motor and drive losses plus reduced pump efficiency make the saving somewhat smaller.
A similar relationship applies to impeller diameter, but it stays accurate only for trims within roughly 10% to 20% of the original diameter. Deeper cuts drop efficiency sharply and need a separate review.