Pump System Curve Calculator & Simulator

H_pump(Q)=H₀−aQ², with a fitted from shutoff head and one user-entered pump-curve reference point. This is an educational approximation, not a general law for centrifugal pumps. Manufacturer-tested curves can deviate materially from a parabola, particularly near shutoff and at high flow.

H_system(Q)=H_static+kQ². The fixed term represents elevation and pressure head. The Q² term is a common screening approximation for turbulent piping systems with fixed geometry; real Darcy-Weisbach friction also depends on Reynolds number, roughness, valve position and liquid properties, so the exponent is not universally exactly two.

For these two quadratic curves, setting H_pump=H_system gives Q_op=√[(H₀−H_static)/(a+k)]. The result is the steady intersection for the assumed fixed pump speed and fixed system resistance. Valve movement, variable-speed control, parallel pumps, transients or changing liquid properties shift the curves and therefore the operating point.

NPSH_A=(P_source−P_vapor)/(ρg)+h_z−h_f,suction. NPSH_A belongs to the system; NPSH_R belongs to the pump and must be supplied by the manufacturer. This page fits NPSH_R with a simple rising quadratic only for screening. NPSH_A>NPSH_R is necessary, but reliable operation also requires the application-specific margin called for by the manufacturer and applicable guidance such as ANSI/HI 9.6.1.

The illustrative efficiency curve is a parabola anchored at the entered BEP efficiency and the entered efficiency at 50% of BEP flow. It is symmetric only because the model is intentionally simple; real pump efficiency curves are not generally symmetric. Hydraulic power is P_hyd=ρgQH and estimated shaft power is P_shaft=P_hyd/η. If the operating point is far outside the efficiency anchors, the power estimate is explicitly flagged as extrapolated.

BEP is the best efficiency point. The preferred operating region (POR) is a pump-specific range around the favorable hydraulic region, and the allowable operating region (AOR) is wider. Their boundaries depend on pump design and service; this simulator therefore reports operating flow as a percentage of BEP but does not invent universal POR/AOR limits.

Not necessarily. The duty point is the flow and head required by the system or specified for the application. The BEP is the point where the pump reaches maximum hydraulic efficiency. A selected duty point may lie near the BEP, but the pump manufacturer defines the BEP and the preferred and allowable operating regions from the actual tested pump curve.

There is no single universal margin such as 0.5 m or 1 m that is appropriate for every pump. NPSH_A should exceed the manufacturer-supplied NPSH_R, and additional margin should be selected for the pump, liquid, service, operating region and site conditions using manufacturer guidance and an applicable standard such as ANSI/HI 9.6.1.

Suction-side friction loss generally increases strongly with flow, reducing the absolute pressure head available at the pump inlet. NPSH_R is a pump characteristic and commonly increases with flow, so the available margin can shrink from both directions. The actual NPSH_R curve should come from the pump manufacturer.

POR is the preferred operating region around the pump’s best efficiency point where hydraulic loading, vibration and reliability are generally most favorable. AOR is the wider allowable operating region. Their limits are pump-specific and should come from the manufacturer or guidance such as ANSI/HI 9.6.3; this simulator does not invent universal POR or AOR limits.

Use it for education and preliminary screening. Final pump selection should use the manufacturer’s tested pump, efficiency, power and NPSH_R curves together with a full hydraulic calculation of the actual system, liquid properties, suction conditions, control strategy and required operating range.