Physics

2.23 - Hydraulics

3 min

note 1 of 3

Pressure is transmitted through an incompressible liquid

Liquids are incompressible - their particles are already closely packed, so a liquid can't be squashed into a smaller volume.
When a force is applied to an enclosed liquid, the pressure created is transmitted equally throughout the liquid in all directions.
At every surface the liquid touches, this pressure creates a force at right angles (normal) to the surface.

A blue cube sits in a tank of liquid with a wavy surface, and four arrows point inwards at it from above, below and both sides, all labelled pressure.

note 2 of 3

A hydraulic system multiplies force

A hydraulic system uses transmitted pressure in an enclosed liquid to act as a force multiplier, turning a small input force into a larger output force.
Because the liquid transmits pressure equally, the pressure at both pistons is the same.

How the force is multiplied

A force applied to a small piston creates pressure in the liquid: $p = \frac{F}{A}$ .
That same pressure is transmitted through the liquid to a large piston.
At the large piston, the pressure acts over a larger area ( $F = p \times A$ ), producing a larger force.
The larger the area of the second piston compared with the first, the greater the force multiplication.

Two pistons joined by liquid in a U-shaped container, a downward arrow labelled force on the narrow piston 1 and four upward arrows labelled force under the wide piston 2.

note 3 of 3

Worked example - Force on the second piston

A simple hydraulic system has two pistons connected by an enclosed liquid. A force of 15 N is applied to the first piston, which has a cross-sectional area of 0.0005 m². The second piston has a cross-sectional area of 0.0025 m². Calculate the force acting on the second piston.

A narrow piston pushed down by an arrow labelled 15 N sits left of a wider piston raised by four upward arrows, both in one container of liquid, labelled 0.0005 m² and 0.0025 m².

Step 1 - Find the pressure at the first piston

Use the force and area of the first piston in $p = \frac{F}{A}$ .

$p = \frac{F}{A} = \frac{15}{0.0005} = 30,000 Pa$

Step 2 - Find the force at the second piston

The pressure is transmitted equally through the liquid, so the pressure at the second piston is the same as at the first: 30,000 Pa.

Rearrange to $F = p \times A$ and use the area of the second piston.

$F = p \times A = 30,000 \times 0.0025 = 75 N$

The 15 N input force has been multiplied to a 75 N output force.

key terms

TermDefinition

IncompressibleUnable to be squashed into a smaller volume because the particles are closely packed.

Force multiplierA device that turns a small input force into a larger output force.

end of notes

Key points to remember

Pressure is transmitted through an incompressible liquid

Liquids are incompressible - their particles are already closely packed, so a liquid can't be squashed into a smaller volume.

When a force is applied to an enclosed liquid, the pressure created is transmitted equally throughout the liquid in all directions.

At every surface the liquid touches, this pressure creates a force at right angles (normal) to the surface.

A hydraulic system multiplies force

A hydraulic system uses transmitted pressure in an enclosed liquid to act as a force multiplier, turning a small input force into a larger output force.

Because the liquid transmits pressure equally, the pressure at both pistons is the same.

How the force is multiplied

A force applied to a small piston creates pressure in the liquid:

p = \frac{F}{A}

That same pressure is transmitted through the liquid to a large piston.

At the large piston, the pressure acts over a larger area (

F = p \times A

), producing a larger force.

The larger the area of the second piston compared with the first, the greater the force multiplication.