Scale duty with speed: Q with N, H with N squared, P with N cubed. Re-intersect the system curve and recheck motor, NPSH, and shutoff.
The three scaling laws
Capacity scales with the speed ratio, head with its square, power with its cube, at constant efficiency and diameter. Impeller trim follows the same laws approximately for cuts under about 10%.
Why a VSD saves energy
A 17% slowdown cuts power by roughly 43% before efficiency drift, because the cube dominates. Savings vanish against mostly-static-head systems, so check the static-to-friction split first.
Recheck before accepting
Re-intersect H = H_static + kQ^2, confirm motor turndown and cooling, recheck NPSH margin at lower flow, and never plan operation near shutoff.
Formulas
Affinity laws
Q2 = Q1(N2/N1); H2 = H1(N2/N1)^2; P2 = P1(N2/N1)^3
Constant diameter and efficiency assumed.
System intersection
H = H_static + kQ^2
The pump rides back along this curve.
Worked example
2900 to 2400 rpm
Inputs: Q 100; H 30; P 11.67.
Calculation: Q2 82.76; H2 20.54; P2 6.62.
Frequently asked questions
What changes with speed?
Flow linear, head square, power cube of speed ratio.
Why does a VSD save energy?
Small slowdowns give cubic power savings, minus efficiency drift.
Do I need the system curve?
Yes: re-intersect it; the pump rides back along it.
Sources and further verification
- Affinity laws — Wikipedia
- Centrifugal pump — Wikipedia
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