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Pressure

11 min read

What is pressure?

Pressure tells us how concentrated a force is. A sharp knife cuts easily because the force acts on a tiny area. A camel's wide feet do not sink in sand because the force is spread over a big area.

Pressure = force ÷ area. The unit is the pascal (Pa): 1 Pa = 1 N/m².
  • pressure (Pa)
  • force acting at right angles to the surface (N)
  • area of contact (m²)
Try itPress on the sand

Keep the force the same and make the area smaller. The pressure rises and the object sinks deeper.

Worked examplePressure of a block

A block weighs 120 N and rests on a face of area . What pressure does it exert?

  1. Use P = F ÷ A.

Answer: The pressure is 300 Pa.

Pressure in liquids

Pressure at depth h in a liquid of density ρ.
  • density of the liquid (kg/m³)
  • 9.8 N/kg
  • depth below the surface (m)
Pressure increases with depthA tank of water with arrows pushing sideways on the wall. The arrows are longer deeper down, showing that liquid pressure increases with depth. The pressure at depth h is rho times g times h.hdeeper:bigger pushP = ρ g hacts in all directions
Try itDive deeper

Pressure in water grows steadily with depth. Divers feel it on their ears. This is the pressure from the water alone; add atmospheric pressure (about 100 000 Pa) for the total.

Pressure passes through a liquid: the hydraulic press

Pressure applied to a liquid in a closed space is passed on equally in every direction (Pascal’s principle). A small force on a small piston makes a pressure that pushes a big piston with a big force. Car lifts, garage jacks and the brakes of a vehicle all work this way.

A hydraulic pressTwo pistons joined by a tube of liquid. A small force on the small piston creates a pressure in the liquid that pushes a large piston upwards with a much bigger force, because the pressure is the same everywhere.F₁ = 10 NF₂ = 100 Nsmall area A₁large area A₂ = 10 × A₁same pressure everywhere: F₁ ÷ A₁ = F₂ ÷ A₂
Worked exampleA garage jack

A force of 50 N pushes a small piston of area 0.002 m² in a hydraulic jack. The large piston has area 0.04 m². What force does the large piston give?

  1. The pressure is the same on both pistons.
  2. Force on the large piston.

Answer: The large piston gives a force of 1 000 N: twenty times the effort.

Each extra metre of depth adds about 9 800 Pa. The bars grow in equal steps.
Check yourself Which change would INCREASE the pressure of a book on a table?
Check yourself What is the pressure at 10 m depth in water (ρ = 1 000 kg/m³, g = 10 N/kg)?

Key terms

Pressure
Force per unit area.
Pascal (Pa)
The unit of pressure: one newton per square metre.
Atmospheric pressure
The pressure of the air around us, about 100 000 Pa at sea level.

Summary

  • P = F ÷ A: same force on a smaller area gives more pressure.
  • Liquid pressure P = ρgh increases with depth and density.
  • Liquid pressure acts equally in all directions.
  • A hydraulic press passes pressure through a liquid equally, so a small force on a small piston makes a large force on a large piston.
Structure and Properties of Matter Work, Energy and Power