Pump head pressure:
turning metres of water into kPa and bar

Head is pressure expressed as a height

A pump datasheet might say it can lift water to 30 m. A pressure gauge on the same pump reads in kilopascals or bar. Both describe the same physical thing: how hard the pump can push. Head is the height of a column of fluid that the pressure can support, so it is a way of writing pressure without involving the fluid's weight.

Using head has a handy benefit. A given pump produces the same head with water, oil or brine, but the pressure it generates changes with the fluid density. Quoting head lets one curve describe the pump, and the pressure follows when the fluid is known.

For ordinary water, near 1000 kg/m³, the conversion is so regular that most people remember it: about 10 m of head is about 1 bar.

The formula and the 10 m example

Turn it around when you have a gauge reading and want the head: h = P ÷ (ρ × g). At 100 kPa that is 100,000 ÷ 9,810 = 10.2 m of water.

A quick table for water

The table scales in a straight line, so any head can be found by multiplying by 9.81 and dividing by 100 to get kPa, for example 25 m × 9.81 = 245.25 kPa. If the liquid is not water, scale by its specific gravity: a fluid at 1.2 times the density of water gives 1.2 times the pressure for the same head.

Using the conversion on a building

The conversion is most useful for tall buildings and tanks. A tank on a roof 25 m above a tap gives that tap a static pressure of 25 × 9.81 = 245.25 kPa, a little under 2.5 bar, before any flow starts. Once water runs, friction in the pipes reduces what is left at the tap.

The same arithmetic tells you the lowest level a tank can feed. A fixture that needs 100 kPa to work properly must sit at least 100 ÷ 9.81 = 10.2 m below the water surface, with extra height to cover friction losses and a margin for the water level falling in the tank.

What head a pump has to supply

The head a pump must deliver is the sum of several parts, not just the height. The static lift is the vertical rise from the water source to the outlet. Friction loss is the head consumed by pipe walls, bends and valves, and it grows with flow. Any pressure needed at the outlet, such as for a sprinkler or a boiler feed, adds a further amount.

• Static head: vertical distance between the suction level and the discharge level.
• Friction head: losses in pipes, valves and fittings at the design flow.
• Pressure head: the pressure required at the outlet, converted to metres.
• Total dynamic head: the sum of the three, which is the figure to compare against the pump curve.

Because friction depends on the flow, a pump's operating point sits where its curve crosses the system curve. The simple pressure formula converts each piece of the sum, but it does not predict friction, which needs pipe size, length and roughness.

Suction lift and its limit

Pumps that sit above the water they draw cannot pull water up indefinitely. Atmospheric pressure of about 101 kPa is the push that raises the water, and a perfect vacuum would hold up a column of around 10.3 m. Real pumps manage much less because the water starts to form vapour bubbles, known as cavitation, and because of friction in the suction pipe.

• Keep the suction pipe short, large and straight to limit friction losses.
• Position the pump as close to the water level as the installation allows.
• Warmer water vaporises more easily, so the practical lift falls as temperature rises.
• At high altitude the atmospheric pressure is lower, which also lowers the usable suction lift.

Datasheets give a required net positive suction head, or NPSH, and the installation must provide more than that figure. The same pressure and head conversion applies, but the values are in absolute pressure terms.

From head and flow to pump power

Once the head is known, the power needed follows with the flow. Hydraulic power is density × gravity × flow × head. The shaft power is greater by the pump efficiency.

Motors, wiring and starting conditions need their own margins on top, so use these figures as the starting point for a proper selection. A general mechanical capacity-planning tool can help organise the related sums, though the pressure and power conversion above is the key step.

Slips that distort head and pressure figures

Three slips account for most wrong answers. The first is mixing units, using kilopascals where the formula needs pascals, which produces a result a thousand times off. The second is using the pump's maximum head as if it were available at every flow, when the curve falls as flow rises. The third is forgetting the fluid: a brine, glycol mix or sludge is denser than water, so the pressure for a given head is higher.

Write the unit beside every figure and sanity-check against the rule of thumb that 10 m of water is close to 1 bar. If a worked answer disagrees with that by a large factor, an input or a unit is wrong.