Pressure: Complete O Level Physics Cheatsheet
O Level Physics, Chapter 7 · Read time: ~8 minutes
These notes come from TGC Academy's O Level Physics tuition in Singapore.
What is the formula for pressure?
Pressure is the force acting normally per unit area: P = F / A, measured in pascals (Pa), where 1 Pa = 1 N/m². In a liquid, the pressure at depth h is P = ρgh.
Key Formulas
Pressure on solids
Pressure is the force acting normally (perpendicular) per unit area: P = F/A. The same force spread over a larger area gives a smaller pressure, and concentrated on a smaller area gives a larger pressure.
Small area, large pressure: knives, nails and needles are sharp so a small force produces a large pressure that can cut or pierce. Large area, small pressure: tractors have wide tyres and snowshoes are broad so they don't sink into soft ground.
Unit: pascal (Pa), equal to N/m². Watch for areas given in cm²: 1 cm² = 1 × 10⁻⁴ m², not 10⁻² m².
Trap: Converting cm² to m² is the most common slip in this chapter. Since area is squared, 1 m² = 100 cm × 100 cm = 10 000 cm². Dividing by 100 instead of 10 000 makes your answer 100 times too small.
Pressure in liquids
Pressure in a liquid increases with depth, and depends only on the depth h, the liquid's density ρ and g: P = ρgh. It does not depend on the shape or width of the container.
At any point in a liquid, pressure acts equally in all directions. This is why water spurts sideways out of holes in the side of a bottle, and spurts further from the lower holes where the pressure is greater.
A dam is built thicker at the bottom because the water pressure, and so the force on the dam wall, is greatest at the greatest depth.
Trick: If a question shows several oddly shaped containers filled to the same height with the same liquid, the pressure at the base is the same in all of them. Only depth and density matter, so you can answer without any calculation.
Atmospheric pressure, manometers and hydraulics
The atmosphere exerts a pressure of about 1.0 × 10⁵ Pa at sea level, because of the weight of the air above us. A mercury barometer measures it as the height of a mercury column it can support, about 760 mm at sea level.
A manometer is a U-tube of liquid used to measure gas pressure. The difference in liquid levels, h, shows how much the gas pressure is above (or below) atmospheric pressure: gas pressure = Pₐₜₘ + ρgh.
In a hydraulic system, a liquid (which is almost incompressible) transmits pressure equally throughout. A small force on a small piston creates a pressure that acts on a large piston, producing a much larger force: F₁/A₁ = F₂/A₂. This is how a car jack or hydraulic brakes work.
Trap: In a manometer, the height difference h is the vertical difference between the two liquid surfaces, not the length of liquid in one arm. Also, the gas is on the side where the liquid has been pushed down.
Worked Example
A diver is swimming 12 m below the surface of a lake. The density of the water is 1000 kg/m³, atmospheric pressure is 1.0 × 10⁵ Pa, and g = 10 m/s².
(a) Calculate the pressure on the diver due to the water alone. [2]
P = ρgh
= 1000 × 10 × 12
= 1.2 × 10⁵ Pa
(b) Calculate the total pressure acting on the diver. [1]
Total pressure = Pₐₜₘ + ρgh
= 1.0 × 10⁵ + 1.2 × 10⁵
= 2.2 × 10⁵ Pa
(c) The glass window of the diver's mask has an area of 0.015 m². Calculate the force on the outside of the window due to the total pressure. [2]
F = P × A
= 2.2 × 10⁵ × 0.015
= 3.3 × 10³ N
Why this question is a good test of the topic: part (a) and part (b) look almost identical, and many students forget to add atmospheric pressure when the question asks for the total. Reading the exact wording of what's being asked is worth as many marks as the formula itself.
Frequently Asked Questions
What is the formula for pressure in O Level Physics?
P = F/A, where F is the force acting normally on the surface and A is the area. The unit is the pascal (Pa), equal to N/m².
Does liquid pressure depend on the shape of the container?
No. Liquid pressure depends only on depth, the liquid's density and g (P = ρgh), not on the shape or width of the container.
Why are dams thicker at the bottom?
Water pressure increases with depth, so the force on the dam wall is greatest at the bottom. A thicker base withstands that larger force.
How does a hydraulic jack produce a large force?
Pressure is transmitted equally through the liquid. A small force on a small piston creates a pressure that acts on a much larger piston, producing a larger force, since F = P × A.
What does a manometer measure?
A manometer measures the pressure of a gas relative to atmospheric pressure, using the height difference between the liquid levels in a U-tube.
Still losing marks on pressure questions?
Small group O Level Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.