Pump Curve Simulator: Operating Point, Efficiency & System Matching

simulator intermediate ~10 min
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Q_op = 35.4 L/s at H = 32.5 m — stable operating point

A pump with 50 m shutoff head meets a system with 15 m static head and K = 0.014 s²/m⁵ at Q = 35.4 L/s and H = 32.5 m. Pump efficiency at this point is approximately 82%, consuming 13.8 kW of shaft power.

Formula

H_pump = H₀ × (1 − (Q/Q_r)²) (parabolic pump curve)
H_system = Hs + K × Q² (system resistance curve)
P = ρ × g × Q × H / η (shaft power)

Pump Meets Pipe

A centrifugal pump converts shaft rotation into fluid pressure and flow. But the actual flow delivered depends not only on the pump but on the piping system it serves — pipe lengths, diameters, fittings, valves, and elevation changes all create resistance. The operating point is where the pump's capability exactly matches the system's demand, found graphically at the intersection of the pump curve and the system curve.

The Pump Curve

Pump manufacturers characterize each pump with an H-Q curve showing head versus flow at a fixed speed. At shutoff (Q = 0), all energy goes into pressure (maximum head). As flow increases, more energy goes into kinetic energy and internal losses, reducing the available head. The curve shape depends on impeller geometry — radial impellers give steep curves, mixed-flow impellers give flatter ones.

The System Curve

The system curve H_system = Hs + KQ² has two components. Static head Hs (elevation difference plus any pressurized vessel pressure) is constant regardless of flow. The dynamic component KQ² represents friction and minor losses, which scale with the square of velocity (and hence flow). Closing a valve increases K, shifting the system curve up and reducing flow; opening it does the opposite.

Efficiency & Energy

Pump efficiency peaks at the best efficiency point (BEP) — the flow rate the pump was designed for. Shaft power P = ρgQH/η rises steeply with flow. Operating far from BEP wastes energy and shortens pump life through vibration and cavitation. Variable-speed drives (VSDs) shift the pump curve to match varying demand, maintaining efficiency across a range of operating conditions. This simulator overlays pump and system curves to find the operating point and reports the efficiency and power consumption.

FAQ

What is a pump curve?

A pump curve (or H-Q curve) plots the head (pressure rise) a pump can deliver versus the flow rate. At zero flow (shutoff), head is maximum; as flow increases, head decreases. The curve is determined by pump geometry and speed. Manufacturers provide these curves from laboratory testing.

What is the system curve?

The system curve plots the total head required to push fluid through the piping system versus flow rate: H_system = H_static + K×Q². Static head accounts for elevation change, and K×Q² represents friction and minor losses that increase with the square of flow.

How is the operating point determined?

The operating point is where the pump curve intersects the system curve — the unique combination of flow and head where the pump output exactly matches the system demand. Changes in system resistance (valve throttling, pipe aging) shift the system curve and move the operating point.

What is BEP and why does it matter?

BEP (Best Efficiency Point) is the flow rate where pump efficiency peaks. Operating within ±10-20% of BEP ensures low vibration, long bearing life, and minimum energy cost. Chronic operation far from BEP causes premature wear, noise, and wasted energy.

Sources

Embed

<iframe src="https://homo-deus.com/lab/hydraulics/pump-curve/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub