Pump and system curve
A pump does not deliver its rated flow — it delivers whatever the system allows. This intersects the pump curve with the system curve, reports the real operating point and power, and shows what a speed change does through the affinity laws.
| Quantity | Value | Unit |
|---|---|---|
| Shut-off head (scaled) | 40.0 | m |
| Rated flow (scaled) | 20.0 | L/s |
| Rated head (scaled) | 30.0 | m |
| Operating flow | 25.82 | L/s |
| Operating head | 23.33 | m |
| Hydraulic power | 5.91 | kW |
| Shaft power | 8.21 | kW |
The pump curve is fitted as H = H0 − a·Q² through shut-off and the rated point.
H = H₀ − a·Q² · Fitted through shut-off and the rated point.
H = H_static + k·Q² · k is the design loss over the design flow squared.
Q ∝ N, H ∝ N², P ∝ N³ · The reason a variable-speed drive saves so much power.
A clear path from inputs to results.
A pump does not deliver its rated flow; it delivers whatever the system allows. The operating point is where the two curves cross, and that is the only flow the pump will actually run at.
How to use
- Enter the shut-off head and the rated point.
- Set the static lift and the system loss coefficient.
- Read the operating flow, head and shaft power, then change the speed to see the affinity effect.
The formula
Reference: Quadratic pump and system curves; affinity laws Q ∝ N, H ∝ N², P ∝ N³.
Worked example
40 m shut-off, 30 m at 20 L/s, 10 m static
- k = 0.02 m/(L/s)².
- 1
a = 10/400 = 0.025. Q² = 30/0.045 = 667 → Q = 25.8 L/s. H = 23.3 m. Hydraulic power 5.9 kW.
25.8 L/s at 23.3 m, 5.9 kW hydraulic.
Interpreting the result
Because power scales with the cube of speed, a 20% speed reduction takes about half the power — which is why variable-speed drives pay for themselves on any part-load system.
Assumptions & limitations
- Quadratic curves, which fit the normal range of a centrifugal pump.
- Efficiency is constant at the stated value.
- No NPSH or cavitation check.
- The system curve has a single loss coefficient.
Frequently asked questions
Why is my measured flow lower?
The real system usually has more loss than k·Q² suggests — fouling, fittings and control valves.
Does throttling save energy?
Almost none — it adds system loss. A VFD removes the loss instead.
What is the best efficiency point?
The rated point, usually. Running far from it causes recirculation and vibration.
Why does the head fall with flow?
Because the velocity triangles in the impeller give less head as flow rises.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.