How a pump's useful power depends on flow and head, how efficiency enters in, and what the operating point means.
Introduction
A pump adds energy to the water by raising the pressure. The useful (hydraulic) power depends on how much water is moved and how great a head is overcome.
The formula
This is the power the pump actually delivers to the water. The pump itself loses some along the way (friction, leakage flow, etc.), which is accounted for via the efficiency η.
Worked example
A flow of 0.5 l/s (= 0.0005 m³/s) at 12 m head gives P_hyd = 1000 · 9.81 · 0.0005 · 12 ≈ 59 W. With η = 0.6, the shaft power becomes ≈ 98 W.
The operating point
- 01The pump's performance is described by a pump curve (H as a function of Q).
- 02The system's resistance is described by a system curve; the intersection point is the operating point.
- 03Efficiency is not constant — it varies along the curve and is read off at the operating point.
Pump control in practice
Modern circulation pumps are speed-controlled (frequency-driven) and can follow different control curves. The choice determines both comfort and electricity consumption, and it is about how the pump responds when the thermostatic valves close and open.
- 01Constant curve (fixed RPM): the pump runs unchanged regardless of demand — simple, but uses unnecessary energy and can cause fan noise at low load. Typically used for underfloor heating with constant flow.
- 02Constant pressure: the pump maintains the same lift height regardless of flow — suitable for systems with low pipe loss and many circuits, e.g. radiator systems with short strings.
- 03Proportional pressure: the lift height is reduced as flow decreases — suited to systems with long distribution networks where pipe loss dominates, and saves most electricity at part load.
Affinity laws — why frequency control saves so much
The reason a speed-controlled pump saves so much electricity lies in the affinity laws. When the speed n changes, flow, head and power each follow their own power of the ratio — and especially power reacts dramatically.
If the pump runs at half speed in periods with low heat demand, it thus uses only one-eighth of the power — 100 W becomes just 12 W. That is what makes proportional and constant-pressure control so effective: when thermostat valves close and flow demand decreases, the pump reduces the speed, and a modest reduction in flow gives a large reduction in power consumption. The laws apply exactly only at unchanged efficiency and for the pure pipe-loss part of the system curve; a static lift (open installations) changes the picture, but in closed heating circuits without static lift they hit the mark — and explain why the old fixed-speed pumps used so much more power than today's controlled ones.
Energy requirements — EEI and ecodesign
Circulation pumps are covered by the EU's ecodesign requirements, which have cleared the old power-hungry fixed-speed pumps from the market. Efficiency is expressed by the Energy Efficiency Index (EEI) — the lower, the better.
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