Engineering calculators · Pumping

Pump head, NPSH and power calculator

Size a pump for a water system from the suction tank to the delivery point. Enter both pipe runs, their fittings, the tank levels and pressures, and the calculator works out the total dynamic head, the NPSH available against the pump’s NPSHr, the pressure at each pump flange, and the power and yearly energy cost. Add three points from a pump curve to find where the pump will actually run, including at reduced speed on a variable-speed drive.

Flow and water Design flow Water temperature, °C Site altitude, m

Suction side Internal diameter, mm Pipe length, m Material Roughness k, mm Liquid level above pump, m Tank surface pressure, kPa(g)

Discharge side Internal diameter, mm Pipe length, m Material Roughness k, mm Delivery level above pump, m Delivery surface pressure, kPa(g)

Levels are measured from the pump centreline: a negative suction level means the pump lifts from below. Use 0 kPa for a tank open to air, or the gauge pressure of a closed vessel. For a pipe that discharges freely to air, set the delivery level to the outlet height and keep one exit loss.

Fittings Loss coefficients to use

Fitting	K range	K used	Suction, no.	Discharge, no.
Standard 90° elbow	0.21–2	1.11
Long-radius 90° elbow	0.07–1	0.535
Standard 45° elbow	0.2–0.4	0.300
Long-radius 45° elbow	0.14–0.21	0.175
Tee	0.1–2.4	1.25
Gate valve, fully open	0.03–0.8	0.415
Globe valve, fully open	5.5–14	9.75
Swing check valve, fully open	2–5.1	3.55
Entrance from tank (sharp-edged)	0.42	0.420
Exit into tank or open discharge	1	1.00
Other losses, sum of K (strainers, meters, manufacturer data)
Total K			1.94	9.39

Pump and energy Pump efficiency, % Motor efficiency, % NPSH required, m Running hours a year Electricity price, £/kWh

Pump curve (optional) Shut-off flow, m³/h Shut-off head, m Mid flow, m³/h Mid head, m End flow, m³/h End head, m Speed, % of curve speed

Results

Total dynamic head19.7 m1.93 bar across the pump

NPSH available12.0 m8.97 m above NPSHr

Motor input power4.16 kWshaft 3.83 kW, hydraulic 2.68 kW

Energy cost a year£4,16416,657 kWh, 0.0833 kWh/m³

Pump and system curves

System curve Pump at set speed Pump at 100% (when slowed) Design duty Operating point

Operating point: 54.2 m³/h at 20.8 m, drawing about 4.77 kW at the efficiencies above.

Quantity	Suction	Discharge	Notes
Velocity	0.786 m/s	1.77 m/s	Q / (πD²/4)
Reynolds number	117,486	176,229	ρvD/μ
Darcy friction factor	0.01746	0.01615	Colebrook-White, or 64/Re when laminar [dff]
Pipe friction loss	0.0183 m	5.15 m	f (L/D) v²/2g
Fittings loss	0.0611 m	1.50 m	ΣK v²/2g [clark]
Pressure at pump flange	18.5 kPa(g)	210 kPa(g)	Static pressure at the inlet and outlet

Head build-up and NPSH	Value	Notes
Static lift	13.0 m	Delivery level − suction level
Surface pressure difference	0 m	(p_delivery − p_suction) / ρg
All pipe and fitting losses	6.72 m	Suction + discharge
Total dynamic head	19.7 m	Sum of the three rows above
Atmospheric pressure at site	100.7 kPa	Standard atmosphere at the site altitude [atm]
Vapour pressure of water	2.34 kPa	At the water temperature [NIST]
Water density / viscosity	998.2 kg/m³ / 1.002 mPa·s	[NIST]
NPSH available	12.0 m	(p_atm + p_suction − p_vapour)/ρg + suction level − suction losses [npsh]

How the calculation works

Pipe losses. Each side is a single pipe run. Friction uses Darcy-Weisbach with a Colebrook-White friction factor (64/Re when laminar), and fittings add ΣK × v²/2g. This is the same method as the pipe pressure drop calculator. Water density and viscosity come from NIST at the water temperature [NIST].
Fitting K values are published ranges [clark]. Real values depend on size, make and whether a fitting is screwed or flanged, so choose the low, middle or high end, and use the manufacturer’s figure where you have one. The entrance from a tank is treated as a sudden contraction (K = 0.42) and the exit into a tank as K = 1, which also accounts for the velocity head of a free discharge.
Total dynamic head = static lift + surface pressure difference + suction losses + discharge losses. This is the head the pump must add at the design flow.
Pump flange pressures come from Bernoulli along each line: the pressure at the tank surface, plus or minus the level, minus losses and the velocity head in the pipe.
NPSH available = (atmospheric + suction surface gauge pressure − vapour pressure) / ρg + suction level − suction losses [npsh]. Atmospheric pressure falls with altitude, from the standard-atmosphere barometric formula [atm], and vapour pressure rises steeply with temperature [NIST]. A margin of at least 0.6 m over the pump’s NPSHr, and preferably 1.5 m, is commonly recommended [npsh].
Power. Hydraulic power = ρ g Q H. Shaft power divides by pump efficiency and motor input divides again by motor efficiency. Yearly energy = motor input × running hours.
Operating point. A pump runs where its curve crosses the system curve, not at the design duty. The three curve points are fitted with a quadratic, H = a + bQ + cQ². At a different speed the curve is scaled by the affinity laws (Q ∝ N, H ∝ N²) [aff], and the crossing is found numerically. The power at the operating point assumes the same efficiencies, which is only approximate away from the pump’s best efficiency point.

What this cannot tell you. It models one suction line and one discharge line in series, carrying clean water at steady flow. It does not handle branched networks, parallel pumps, sludge or other non-Newtonian liquids, entrained air, or surge and water hammer. A three-point quadratic is only a fit of the real pump curve, and it cannot predict efficiency or NPSHr across the curve. Use the manufacturer’s full curves to confirm the selection.

Sources

← All engineering calculators