Affinity laws predict the new duty after a speed change or small impeller trim: flow follows N, head follows N squared, power follows N cubed. Slowing 2900 to 2400 rpm scales flow by 0.828, head by 0.685, and power by 0.567, which is why variable-speed drives save energy. Always re-intersect the system curve and recheck NPSH at the new point.
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.
Lesson:
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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