Pump Operating Point Calculator (Pump Curve Meets System Curve)
The flow and head a pump will really deliver in a given pipe system, from its shut-off head and one rated point and the system's static head and friction loss, with both curves drawn.
Results
The dashed line marks the value you entered.
What this tool does
A pump does not deliver its rated flow, it delivers where its own curve crosses the system curve: the static head to be overcome plus a friction loss that grows with the square of the flow. Here the pump curve is a parabola H = H₀ − aQ² through the shut-off head and one rated point, which is a good fit over the useful middle of a centrifugal pump's curve; the system curve is H = H_static + KQ². Closing a valve steepens the system curve and moves the point left; more static lift moves it left too. Keep the point near the pump's best-efficiency flow rather than far to either side.
Formula
pump curve H = H0 − a Q² · system curve H = H_static + K Q² · operating point Q = Q_r √[(H0 − H_static) ÷ ((H0 − H_r) + h_f)]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
h0 | Pump head at zero flow (shut-off head) | m |
hr | Pump head at the rated flow | m |
qr | Rated flow (the point you took the head at) | m³/h |
hs | Static head (lift plus pressure to deliver against) | m |
hf | Friction head loss in the pipework at the rated flow | m |
ef | Pump efficiency at the duty point | % |
q | Flow at which to read the two curves | m³/h |
QO | Flow you will actually get | m³/h |
HO | Head at the operating point | m |
PH | Hydraulic power (water) | kW |
PS | Shaft power at that point | kW |
HP | Pump head at the flow you chose | m |
HY | System head needed at the flow you chose | m |
Worked example
- Pump head at zero flow (shut-off head)40 m
- Pump head at the rated flow32 m
- Rated flow (the point you took the head at)50 m³/h
- Static head (lift plus pressure to deliver against)15 m
- Friction head loss in the pipework at the rated flow8 m
- Pump efficiency at the duty point70 %
- Flow at which to read the two curves40 m³/h
- Flow you will actually get62.5 m³/h
- Head at the operating point27.5 m
- Hydraulic power (water)4.68 kW
- Shaft power at that point6.69 kW
- Pump head at the flow you chose34.9 m
- System head needed at the flow you chose20.1 m
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.