Pump Head Calculator: Total Head and Motor Power for a Transfer Pump

What it calculates

The calculator screens a water transfer pump: the kind that lifts water from an underground sump to an overhead tank, or from a tank up a riser. From the flow you need, the height and the pipe, it works out the friction loss, the total head, the velocity in the pipe, the hydraulic and shaft power, and a minimum motor rating in kW and HP.

It also gives the duty point (flow at total head), which is the figure a pump supplier needs to select a pump from its curves. The result is a screening number for early planning, checking a quoted pump, or deciding whether an existing line is the bottleneck.

Inputs

Flow is the rate the pump must deliver, in litres per minute. For a tank-filling pump it is usually set by how quickly the overhead tank must refill.

Static head is the vertical height from the pump, or from the lowest water level in the sump, to the highest outlet: the overhead tank inlet or the top of the riser.

Pipe internal diameter is the bore of the delivery pipe in millimetres. Use the actual internal diameter from the pipe maker's table, not the nominal size; the two differ, and the difference matters a lot in this formula.

Pipe length is the length of the delivery run, horizontal and vertical together.

Pipe material sets the Hazen-Williams C, a measure of how smooth the pipe is.

Residual pressure at the outlet is zero for a free discharge into a tank. Add head here if the water must arrive at a pressure, for example to feed a fixture directly.

The assumptions panel holds the C value itself, the fittings allowance, the pump efficiency and the motor margin.

Method

1. Flow Q (m³/s) = LPM ÷ 60,000, and diameter D (m) = mm ÷ 1,000.
2. Equivalent length Le = pipe length × (1 + fittings allowance).
3. Friction loss hf (m) = 10.67 × Le × Q^1.852 ÷ (C^1.852 × D^4.87). This is the Hazen-Williams formula in SI units, valid for water at ordinary temperatures.
4. Velocity v = Q ÷ (π × D² ÷ 4). The calculator warns above 3 m/s.
5. Total head H = static head + hf + residual pressure.
6. Hydraulic power (kW) = 9.81 × Q × H, which is density × gravity × flow × head for water.
7. Shaft power = hydraulic power ÷ pump efficiency.
8. Motor rating = shaft power × (1 + motor margin). HP = kW ÷ 0.746.

Assumptions

The fittings allowance is the roughest of these. A short run with many bends and valves can lose more in its fittings than in its straight pipe, while a long straight riser loses little. A designer counts each fitting and adds its own equivalent length. Pump efficiency varies widely with size and with how close the duty point is to the pump's best efficiency point; replace the default with the value from the pump curve once a pump is shortlisted.

Limitations

• It covers one pipe size at one flow. Real systems often change size along the run; each section's loss is calculated and added.
• It ignores suction-side conditions. A pump lifting from below its own level has a suction lift limit, and its net positive suction head must be checked against the pump's requirement.
• Hazen-Williams has a limited range. It is meant for clean water at ordinary temperatures. Hot water, other fluids and very small pipes need the Darcy-Weisbach method.
• It gives a minimum motor rating, not a pump selection. The pump must be chosen so the duty point sits on its curve near its best efficiency point.
• It does not size fire pumps or pressure booster systems. Those follow their own design rules and need a designer's calculation.

Worked example

A pump delivering 200 LPM (12 m³/h) up a 30 m static lift, through 60 m of CPVC pipe with a 50 mm bore, with the default 30% fittings allowance, 60% efficiency, 15% motor margin and a free discharge into the tank:

The duty point to give a pump supplier is 200 LPM at 34.4 m total head, about 3.37 bar. The minimum motor rating is 2.15 kW, or 2.89 HP, so the next standard motor size above that figure is chosen. Friction is about 5.6 m for each 100 m of pipe, and the velocity of 1.7 m/s is comfortably below the 3 m/s warning.

Two changes show what the calculator is for. If the same line were old, scaled GI pipe (C = 100), the friction loss would rise to 9.22 m and the motor to 2.46 kW. If the bore were 40 mm instead of 50 mm, the friction loss would be 12.9 m, the velocity 2.65 m/s and the motor 2.69 kW, with the pump working harder for the life of the building because of one size of pipe.

How engineers use it

A plumbing engineer starts from the water demand of the building and the storage design, which sets how fast the overhead tank must refill. The flow then sets the pipe size, using velocity limits and an acceptable friction loss, and the head is calculated section by section with each fitting counted. NBC 2016 Part 9 covers the water supply design that this sits within.

With the duty point fixed, the engineer reads the pump makers' curves, picks a pump whose best efficiency point sits close to the duty, checks the suction side, and selects the motor from the pump's power at the duty point and at the end of its curve. Pump performance is tested to standards such as ISO 9906. Where the pump runs on backup power, its motor start is part of the DG set sizing too.

When a professional design must replace it

Use the calculator to check a quoted pump, compare pipe sizes and materials, and see whether an existing line is the problem. Replace it with a design by a qualified plumbing or MEP engineer before a pump is ordered, before pipe sizes are fixed, and whenever the system serves fire protection, pressure boosting, hot water, several outlets at varying demand, or a suction lift. The engineer confirms the duty point, the pump selection and the motor for the actual installation.