Pascal’s principle says pressure applied to an enclosed fluid is transmitted equally through the whole fluid. That equal pressure, acting on different areas, gives different forces.
This lesson is part of SPM Physics pressure. It builds on calculating pressure in solids and liquids.
What does Pascal’s principle say about two pistons?
The pressure at the small piston equals the pressure at the large piston. Since P = F ÷ A, this gives F₁ ÷ A₁ = F₂ ÷ A₂.
The pressure is equal on both sides. It is the force that is larger on the side with the larger area.
Worked example: a hydraulic jack
An original jack has a small piston of area 4 cm² and a large piston of area 200 cm². A force of 50 N pushes the small piston down.
Pressure in the fluid = 50 ÷ (4 × 10⁻⁴) = 1.25 × 10⁵ Pa. The large piston has area 200 cm² = 0.020 m², so the output force is 1.25 × 10⁵ × 0.020 = 2500 N.
The area ratio is 200 ÷ 4 = 50, and the force ratio is 2500 ÷ 50 = 50. You can skip the pressure step with F₂ = F₁ × (A₂ ÷ A₁).
Where does the extra force come from?
The liquid cannot be squeezed, so the volume it loses at the small piston equals the volume it gains at the large piston. A large area means a short movement.
If the small piston moves down 25 cm, the large piston rises 25 ÷ 50 = 0.5 cm. Work in = 50 N × 0.25 m = 12.5 J. Work out = 2500 N × 0.005 m = 12.5 J. The two are equal.
The mistake that costs marks
The common slip is to write “the pressure is multiplied by 50” because the output force is 50 times bigger. The pressure is the same in both pistons.
| Quantity | Small piston | Large piston |
|---|---|---|
| Pressure | 1.25 × 10⁵ Pa | 1.25 × 10⁵ Pa |
| Force | 50 N | 2500 N |
| Distance moved | 25 cm | 0.5 cm |
Check that both areas use the same unit before taking the ratio. A ratio of cm² to cm² works, but mixing cm² and m² does not.
How is this used in a car brake?
Pressing the pedal pushes a small master piston. The pressure passes through the brake fluid to larger pistons at the wheels, which press the brake pads against the discs.
For an original system with a master piston of 2 cm² and a wheel piston of 8 cm², a pedal force of 30 N gives a wheel force of 30 × 8 ÷ 2 = 120 N. The liquid must contain no air bubbles, since air compresses and absorbs some of the pressure.
Check yourself
A hydraulic press has pistons of area 5 cm² and 150 cm². What force on the small piston lifts a load needing 1800 N on the large piston? How far must the small piston move to raise the load 2 cm?
Answer
F₁ = F₂ × (A₁ ÷ A₂) = 1800 × (5 ÷ 150) = 60 N.
The area ratio is 30, so the small piston moves 30 times further: 2 × 30 = 60 cm.
Check the work: 60 N × 0.60 m = 36 J and 1800 N × 0.02 m = 36 J.
What to study next
Pascal’s principle is about pressure in a closed liquid, while buoyancy is about a liquid pushing up on an object in it. Continue with applying Archimedes’ principle.
To practise mixed pressure questions with a teacher, see online one-to-one Physics tuition.