“Just turn the feed pump up” is the most expensive three words on the solids-control skid. Flow rises with speed, but head rises with the square of speed and power with the cube. The affinity laws tell you exactly what a speed change buys — and what it costs at the motor.
The three laws
For a fixed impeller, a centrifugal pump's performance scales with speed by three simple relationships. Flow is proportional to speed. Head is proportional to speed squared. Absorbed power is proportional to speed cubed. That last one is the trap: a modest speed increase to chase a little more cyclone feed head can demand far more power than expected, and either trips the motor or quietly runs it into overload.
Why this matters on the skid
Cyclones live on feed head, and feed head is what you are really adjusting when you change pump speed. But because head goes as the square of speed, a small speed change moves the head a lot — useful when you need to bring a bank back into spray, dangerous when you overshoot and erode apexes. And because power goes as the cube, the feed pump that comfortably ran the desilters at design speed can overload its motor if someone winds it up to force more head. The affinity laws let you size the change before you make it.
The same laws work in reverse for trimming: if a pump is over-delivering and roping-open the apexes, backing the speed down a little drops the flow proportionally, the head faster, and the power fastest of all — often the cheapest optimization on the whole system.
Speed change vs impeller change
The affinity laws above are the speed form, for a fixed impeller on a variable-speed drive. A geometrically similar change — trimming the impeller diameter at fixed speed — follows the same proportionalities with diameter in place of speed, over a limited trim range. On a rig the practical lever is usually speed, via the drive; the point either way is that head and power do not track flow linearly, so intuition based on flow alone will overshoot power every time.
The equation
Affinity laws for a fixed impeller at speeds N1 → N2:
Q2 = Q1 (N2/N1) · H2 = H1 (N2/N1)² · P2 = P1 (N2/N1)³
Q = flow, H = head, P = absorbed power, N = pump speed. Flow scales linearly, head with the square, power with the cube.
Before changing feed-pump speed, run the affinity laws. If you need more cyclone head, a small speed increase delivers it fast (square law) — but check the power (cube law) against the motor rating first. To trim an over-delivering pump, backing the speed off is often the cheapest efficiency gain on the skid.
Common questions
What are the pump affinity laws?
For a fixed impeller, flow is proportional to speed, head to speed squared, and power to speed cubed. They let you predict what a speed change does to a centrifugal pump before you make it.
Why does a small speed increase overload the motor?
Because absorbed power scales with the cube of speed. A 10% speed increase raises power by about 33%, and a 25% increase nearly doubles it — enough to trip or overheat a motor that was fine at the original speed.
Do the affinity laws work for impeller trimming?
Approximately, over a limited trim range, with impeller diameter in place of speed. On a rig the practical lever is usually variable speed, but either way head and power do not track flow linearly.
