Pump Operating Point Calculator

About the Pump Operating Point Calculator

Estimates the operating point where a pump's head-flow curve intersects the system resistance curve, using simple linear/quadratic models.

How to use this calculator

1. Enter the pump curve data and the system curve data, using matching units.
2. Choose the flow range you want to test, so the calculator can compare both curves at the same values of flow.
3. Review the intersection point, because that is the operating point where pump head equals system head.
4. Use the result to check whether the pump will meet the required flow and whether it is working near a good efficiency range.

The formula explained

The calculator finds the flow rate \(Q\) where the pump head \(H_{pump}(Q)\) equals the system head \(H_{system}(Q)\). That intersection gives the operating point, and the corresponding head is the pump's actual working head.

• Q = flow rate
• \(H_{pump}(Q)\) = pump head at flow rate \(Q\)
• \(H_{system}(Q)\) = system head required at flow rate \(Q\)
• H = head, usually in meters or feet
• \(Q_{op}\) = operating flow rate at the intersection

Step by step method

1. Write both relationships, one for the pump curve and one for the system curve.
2. Set \(H_{pump}(Q) = H_{system}(Q)\), because the operating point is where supply matches demand.
3. Solve for \(Q\), then substitute that value back into either curve to find the head.
4. Check that the result is realistic for the pump and the piping system.

Worked example

Problem. A pump curve is \(H_{pump}(Q) = 50 - 0.02Q^{2}\), and the system curve is \(H_{system}(Q) = 10 + 0.01Q^{2}\). Find the operating point.

1. Set the curves equal: \(50 - 0.02Q^{2} = 10 + 0.01Q^{2}\).
2. Combine like terms: \(40 = 0.03Q^{2}\), so \(Q^{2} = 1333.33\).
3. Take the square root: \(Q \approx 36.5\). Substitute back to get \(H = 50 - 0.02(36.5)^{2} \approx 23.3\).

Tips and common mistakes

• Make sure the pump curve and system curve use the same units for flow and head, or the intersection will be wrong.
• If there is more than one intersection, check which one is physically realistic for the pump's normal operating range.

Frequently asked questions