Scale centrifugal pump or fan performance to a new speed. Q scales linearly, H as speed squared, P as speed cubed — the key principle behind VFD energy savings.
Turbomachinery · ScalingSpeed-scaling affinity laws (constant diameter):
Diameter-scaling laws (constant speed, geometric similarity):
Combined scaling (speed and diameter):
VFD (variable frequency drive) energy savings:
| N₂/N₁ | Q ratio | H ratio | P ratio | Power saving |
|---|---|---|---|---|
| 1.00 | 1.00 | 1.00 | 1.000 | 0% |
| 0.90 | 0.90 | 0.81 | 0.729 | 27% |
| 0.80 | 0.80 | 0.64 | 0.512 | 49% |
| 0.70 | 0.70 | 0.49 | 0.343 | 66% |
| 0.60 | 0.60 | 0.36 | 0.216 | 78% |
| 0.50 | 0.50 | 0.25 | 0.125 | 88% |
The cube law for power is why VFDs are so effective in HVAC and pumping systems. Reducing speed by just 20% saves nearly half the power. The affinity laws assume geometric similarity and constant efficiency — they are accurate near the design point but degrade at very different operating conditions.