Affinity laws
Variable speed, affinity laws, and when not to trust them
Last reviewed 21 October 2026.
The affinity laws scale a pump curve. Flow follows speed. Head follows speed squared. Power follows speed cubed, which this page does not plot. The flow you will actually get is where the scaled curve crosses the system curve. Multiplying yesterday’s duty by the speed ratio skips that intersection, and it fails first when static head is most of the head.
CurvePoint’s affinity function is the one in the table. The pump curves are illustrative Lakeshore sheets. They end at a stated maximum catalog flow with about half of shutoff head still on the page. A scaled curve is labeled an estimate. Where the curves do not cross, the cell says there is no operating point.
| System | Speed | CurvePoint intersection | Speed-ratio estimate from the 1750 RPM duty |
|---|---|---|---|
| Mostly static head | 1750 RPM | 671 gpm (42.4 L/s) at 90.6 ft (27.63 m) | 671 gpm at 90.6 ft |
| Mostly static head | 1575 RPM | 459 gpm (29.0 L/s) at 90.3 ft (27.53 m) | 604 gpm at 73.4 ft |
| Mostly static head | 1400 RPM | No operating point | 537 gpm at 58.0 ft |
| Mostly friction | 1750 RPM | 502 gpm (31.7 L/s) at 81.6 ft (24.88 m) | 502 gpm at 81.6 ft |
| Mostly friction | 1575 RPM | 446 gpm (28.1 L/s) at 66.8 ft (20.35 m) | 452 gpm at 66.1 ft |
| Mostly friction | 1400 RPM | 388 gpm (24.5 L/s) at 53.5 ft (16.30 m) | 402 gpm at 52.2 ft |
Illustrative Lakeshore Process Equipment figures from CurvePoint’s own evaluation. Not a sealed calculation.
| Reading at 300 gpm | Head |
|---|---|
| Blend of the 1450 and 1750 RPM illustrations | 80.2 ft (24.43 m) |
| Affinity from the 1750 RPM illustration alone | 78.4 ft (23.89 m) |
| Affinity from 1750 to 1400 RPM (estimate, 20% speed change) | Shutoff 69.1 ft, catalog end 512 gpm at 34.6 ft |
Illustrative Lakeshore Process Equipment figures from CurvePoint’s own evaluation. Not a sealed calculation.
Static head moves the answer off the speed ratio
DOE’s tip sheet on adjustable-speed pumping is the public warning: the new duty is the intersection with the system curve, not a point slid along a speed ratio. The first block of the table is a system whose static head is close to the pump’s shutoff. At 1,750 RPM the intersection and the naive ratio agree, because that row is the starting point. At 1,575 RPM they diverge. At 1,400 RPM the scaled curve no longer reaches the system curve, so CurvePoint reports no operating point, while the ratio still prints a flow and a head. That printed flow is not a duty you can run.
The second block is a line where friction is most of the head. The true intersection and the ratio stay nearer each other, and they still disagree. Use the ratio to sketch a curve. Use the intersection to quote a flow. Throttling, which moves the system curve instead of the pump curve, is compared on the operating-point guide.
Radial vanes, two vanes, and curves you may interpolate
For a radial-vane impeller, closed or semi-open, the affinity sketch is reasonable over a moderate speed change. For a 2-vane open solids-handling impeller the curve shape does not scale as cleanly. Wastewater and slurry pumps are often that second kind, because a wide passage is what lets rags through. Label the scaled curve as estimated, and prefer a published test at the speed you will run. The wastewater example uses that caution on its station curve.
When the manufacturer has published two speeds, interpolate. The blend row takes an illustrative 1,450 RPM curve and an illustrative 1,750 RPM curve, scales both to 1,600 RPM, and reads head at 300 gpm. That head differs from scaling only the faster curve down to the same speed. The difference is the reason to keep both published curves in the file.
Extrapolating far from a single curve is the step to refuse. About 10 to 15 percent of speed is a rule of thumb for how far a one-curve sketch should be trusted. The last row drops 1,750 RPM to 1,400 RPM, a 20 percent change, and keeps the runout head at about half of the new shutoff. The shape is still an estimate. It is not a test, and the line still stops at the catalog end rather than at zero head.
Open the friction-dominated example in the calculator. It is already an affinity estimate a little under the published speed. If the real sheet has two speeds, trace both and let the app interpolate. If it has one, stay close to that speed and say so on the report.