Pump Operating Point and Efficiency Calculator

What is the pump operating point?

A centrifugal pump does not run at a single flow and head: it can sit anywhere along its characteristic curve. Where it actually runs is set by the line it feeds. The head the line demands rises with flow: H = Hs + k × Q², where Hs is the static head (elevation and pressure difference) and k × Q² covers friction and minor losses. The operating point is where the pump curve crosses this system curve.

How to use it

Read a few points off the manufacturer's curve and enter them as flow, head and, where known, efficiency. For the line, enter the static head and the total line loss at one flow you know. The calculator derives k from that, draws both curves and finds the intersection. Points can be joined by straight lines or fitted with a second order curve.

Example

A pump delivers 40, 39, 36, 31 and 24 metres at 0, 10, 20, 30 and 40 m³/h. The static head is 10 metres and the line loses 8 metres at 20 m³/h, so the system curve is H = 10 + 0.02 × Q². With curve fitting the intersection falls at 31.6 m³/h and 30 metres. Efficiency there is about 74 percent and shaft power about 3.5 kW.

Limits

System loss is assumed to grow with the square of the flow, a good approximation in fully turbulent flow. The calculator never goes beyond the curve you entered and warns when the intersection lies past the last point. Speed changes, impeller trimming, pumps in parallel or series, viscosity corrections and NPSH checks are not covered. Final selection belongs with the manufacturer's curves and software.