Pump and system curve calculator: operating point, affinity laws, parallel and series pumps, NPSH available

Fit a pump curve to points read off the maker's chart, build the system curve from static head and pipe friction, and find the operating point with its efficiency and power. Try pumps in parallel or series, a new speed or a trimmed impeller (affinity laws), and check NPSH available against NPSH required.

Keep it one tap away for everyday use.

Pump points
System
Duty point
NPSH

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Pump curve

Flow unit

Points read off the maker's curve: flow, head (m), then optional efficiency (%) and NPSH required (m)

Pumps Change

Head is fitted with a quadratic, H = a + bQ + cQ², efficiency with a quadratic (3 or 4 points) or cubic (5 or more) and NPSH required with a quadratic. Affinity laws: flow scales with the speed or diameter ratio, head with its square and power with its cube. Trimming more than about 10 to 20 % of the impeller makes the diameter rule less accurate. The example pump is made up.

System curve

Static head (m): outlet level minus suction level, plus any pressure difference as head Friction from Friction loss (m) at flow (L/s)

With a known loss the friction grows with the square of the flow, h = k Q². With a pipe, the friction factor comes from Colebrook-White for water at the temperature below.

Suction (NPSH available)

Pressure on the liquid surface (kPa absolute) Water temperature (°C) Static suction head (m): + liquid above the pump, − suction lift Suction pipe loss (m) at L/s below …measured or worked out at (L/s)

Sea-level air is 101.325 kPa; an open tank at altitude has less. Vapour pressure and density of water come from IAPWS-IF97. The suction loss is scaled with the square of the flow to the operating point.

Operating point

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What it does

A centrifugal pump does not deliver a fixed flow. It runs where its pump curve (head it can give at each flow, falling as the flow rises) crosses the system curve (head the pipework needs at each flow: the static lift plus friction, which grows roughly with the square of the flow). This tool finds that operating point (duty point) and tells you what it means:

the flow and head, the pump efficiency and the shaft power there;
how far it is from the pump’s best efficiency point (BEP);
what happens with two or more identical pumps in parallel (more flow) or in series (more head);
the affinity laws for a new speed (for example with a variable speed drive) or a trimmed impeller: flow scales with the ratio, head with its square and power with its cube;
NPSH available at the suction, compared with the pump’s NPSH required, to warn of cavitation.

How to use it

Read four to eight points off the maker’s pump curve and type them: flow, head, and if you have them the efficiency and NPSH required. Paste from a spreadsheet or open a CSV or Excel file. Choose the flow unit.
Choose one pump, or several identical pumps in parallel or series, and any change of speed or impeller diameter.
Describe the system: the static head (difference in liquid levels, plus any difference in surface pressure as head) and the friction, either as a loss you know at one flow, or as a pipe length, diameter, roughness and ΣK.
For the suction, give the pressure on the liquid surface (absolute), the water temperature, the static suction head (negative for a suction lift) and the suction pipe loss.

Worked example

A made-up pump with points from 0 to 50 L/s (42 m at shut-off, 19 m at 50 L/s) works against 15 m of static head with 12 m of friction at 40 L/s. The fitted curve is H = 41.91 + 0.02054 Q − 0.009554 Q² (Q in L/s, R² = 0.9999). The curves cross at 40.33 L/s and 27.20 m. Efficiency there is 71.06 %, so the shaft power is 15.11 kW. The best efficiency point is 31.25 L/s, so the pump runs at 129 % of its BEP flow: it would suit a slightly smaller system head or a bigger pump. With 3 m of suction lift, 0.5 m of suction loss at 40 L/s (0.508 m at the duty flow) and water at 20 °C, NPSH available is 6.604 m against 4.033 m required, a comfortable margin. Slowing the pump from 1450 to 1300 rpm moves the duty to 33.65 L/s at 23.49 m.

Tips

Parallel pumps never give double the flow on a real system, because more flow means more friction. The tool shows the gain.
Pumps like to run near their BEP. Far to the left they recirculate and run hot; far to the right they need more NPSH and may overload the motor.
Hot water has a high vapour pressure, so NPSH available falls fast as the temperature rises.

FAQ

Why a quadratic for the head? Most centrifugal pump curves are close to a parabola over their working range, and a quadratic is the usual fit. Check the R² and the dots on the chart.

Is this enough to select a pump? It is for study and planning, not a substitute for professional judgement. Use the maker’s own curves and data for a final choice.

Where the numbers come from

Pump and system curves, operating point, affinity (similarity) laws, parallel and series operation and net positive suction head: standard pump hydraulics, for example Karassik et al., Pump Handbook, and fluid mechanics textbooks such as White, Fluid Mechanics (methods only).
Pipe friction by Darcy-Weisbach with Colebrook-White, shared with fibub's pipe network tool. Water density and vapour pressure from IAPWS-IF97 (IAPWS release, 2007).
The margin rule of thumb (1 m or 30 %) is a rounded general guideline, not taken from any standard. The example pump curve and system are made up.
Checked against an independent NumPy and SciPy calculation (polyfit, brentq) and the Python iapws package, written for the tests.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.