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

> Pump head is the height of water column a pump must lift against: the static height to the outlet, plus the friction loss in the pipe and fittings, plus any pressure needed at the outlet. Multiplying the flow by the head and by 9.81 gives the hydraulic power in kW; dividing by pump efficiency and adding a motor margin gives a screening motor rating.

## 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

| Assumption | Default | Basis |
| --- | --- | --- |
| Hazen-Williams C | 150 for CPVC or uPVC, 120 for new GI, 100 for old GI | Commonly used design values for each pipe type |
| Fittings allowance | 30% of pipe length | Bends, tees, valves and the non-return valve as extra equivalent length |
| Pump efficiency | 60% | A modest figure for a small centrifugal pump away from its best point |
| Motor margin | 15% | Headroom so the motor is not overloaded if the duty point shifts |

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:

| Step | Calculation | Result |
| --- | --- | --- |
| Flow | 200 ÷ 60,000 | 0.003333 m³/s |
| Equivalent length | 60 × 1.3 | 78 m |
| Friction loss | 10.67 × 78 × 0.003333^1.852 ÷ (150^1.852 × 0.05^4.87) | 4.35 m |
| Velocity | 0.003333 ÷ 0.001963 | 1.7 m/s |
| Total head | 30 + 4.35 + 0 | 34.35 m |
| Hydraulic power | 9.81 × 0.003333 × 34.35 | 1.12 kW |
| Shaft power | 1.12 ÷ 60% | 1.87 kW |
| Motor rating | 1.87 × 1.15 | 2.15 kW |

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.

## Frequently asked questions

### What is the difference between static head and total head?

Static head is only the vertical height the water is lifted. Total head adds the friction lost in the pipe, bends and valves, and any pressure the water must still have at the outlet. A pump selected on static head alone will deliver less flow than expected, because it has to overcome friction as well.

### Why does pipe size change the head so much?

In the Hazen-Williams formula friction loss varies with the pipe diameter to the power of 4.87, so a slightly smaller bore loses far more head. Dropping from a 50 mm to a 40 mm bore at the same flow roughly triples the friction loss in this calculator. Undersized pipe is the most common reason a transfer pump struggles.

### What Hazen-Williams C value should I use?

Smooth plastic pipe such as CPVC and uPVC is usually taken at about 150 and new galvanised iron at about 120. Old or scaled GI pipe is rougher, so a lower value such as 100 is used. The presets fill these values in; change the figure if your pipe maker or designer gives a different one.

### How do I convert pump kW to HP?

Divide kW by 0.746 to get horsepower, or multiply HP by 0.746 to get kW. Motors in India are sold in both units. Choose the next standard motor size above the calculated figure rather than rounding down.

### Can I use this for a fire pump or a pressure booster system?

No. Fire pumps are sized to the firefighting design and its rules for flow, pressure and redundancy, and a hydropneumatic booster system has to deliver a pressure range to many outlets at varying demand. Both need a designer's calculation. This calculator screens a simple transfer duty, such as an underground sump to an overhead tank.

## Sources

- [NBC 2016, Part 9, Section 1](https://www.bis.gov.in/standards/national-building-code/?lang=en) — Plumbing services: water supply
- [ISO 9906](https://www.iso.org/standards.html) — Rotodynamic pumps: hydraulic performance acceptance tests
- [IS 15778](https://standards.bis.gov.in/website/published-standards/department-wise) — CPVC pipes for potable hot and cold water distribution
- [IS 1239 (Part 1)](https://standards.bis.gov.in/website/published-standards/department-wise) — Steel tubes, including galvanised tubes

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Source: https://hagerstone.com/calculators/pump-head-calculator