The affinity laws describe how a centrifugal pump or fan behaves when you change its speed: flow scales directly with speed, head scales with the square of speed, and power scales with the cube of speed. That cube relationship on power is the single biggest reason variable speed drives save so much energy on pumps and fans.
For a given impeller running at a new speed, the affinity laws state:
The same relationships apply, approximately, when you trim an impeller's diameter instead of changing its speed.
Because power follows the cube of speed, small speed reductions produce large energy savings. Halving the speed of a pump cuts its power to one eighth. This is why throttling a valve to reduce flow, which leaves the pump at full speed and wastes the excess as heat and noise, is so inefficient compared with simply slowing the pump. Reducing speed with a drive captures the cube-law saving directly, a core idea in strategies to reduce manufacturing energy costs.
The cube-law saving is greatest when the system is dominated by friction, so its curve passes near the origin. When a system has significant static head, lifting fluid to a fixed height, the pump cannot slow as much before it stops delivering flow, and the real savings are smaller than the ideal cube law suggests. Always apply the affinity laws along the actual system curve, not in isolation.
Realising the saving means running the pump only as fast as the process needs, which is exactly what a variable frequency drive does. If you are weighing how to drive the motor, see soft starter vs VFD, since only a drive captures the affinity-law energy saving. A monitoring platform that trends pump speed, flow and power confirms the saving is real and flags a pump drifting off its efficient point. Fabrico reads that from the line and routes the work when efficiency slips. Book a Fabrico demo to see it.
They relate a centrifugal machine's performance to its speed: flow is proportional to speed, head to speed squared, and power to speed cubed.
Because power scales with the cube of speed, a modest speed reduction gives a large power reduction. Slowing a pump to 80 percent speed cuts power to about half.
Yes. They apply to centrifugal fans and pumps alike, and approximately to impeller diameter trims as well as speed changes.
Because systems with significant static head do not follow the ideal friction-only curve. The pump cannot slow as far, so the achievable saving is less than the pure cube law suggests.
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