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Topic 1 · 1.8

Pressure

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Define pressure as force per unit area and use \( p = \dfrac{F}{A} \).
  • Describe how pressure varies with force and area in everyday examples.
  • Describe how pressure beneath a liquid surface changes with depth and density.
  • Use \( \Delta p = \rho g \Delta h \) for the change in pressure beneath a liquid surface EXTENDED.

📚The physics

Pressure = force ÷ area

\[ p = \frac{F}{A} \]

Pressure is in pascals (Pa), where 1 Pa = 1 N/m2; N/cm2 is also used (1 N/cm2 = 10 000 Pa). The same force on a smaller area gives a larger pressure.

A crate weighing 480 N rests on each of its three faces in turn. On its largest face, 0.12 square metres, the pressure is 4000 Pa; on the 0.08 square metre face, 6000 Pa; on the smallest face, 0.06 square metres, 8000 Pa.
The weight is the same each time; only the area changes.
small area, large pressure: a drawing pin, a sharp knife, stiletto heels, a nail
large area, small pressure: snowshoes, wide tractor tyres, a camel’s feet, building foundations, a backpack’s wide straps

Pressure in liquids

A tall can of water with three holes at different depths. Water spurts out faster from the deeper holes. A box lists that pressure beneath a liquid surface increases with depth, is greater in a denser liquid and acts equally in all directions, and gives the Extended equation delta p equals rho g delta h.
Each jet is drawn for the same drop: the deepest is fastest.

Pressure beneath the surface of a liquid increases with depth and is greater in a denser liquid. It does not depend on the shape or width of the container. That is why dams are thicker at the bottom and divers feel more pressure the deeper they go.

\[ \Delta p = \rho g \Delta h \]

EXTENDED ρ is the density of the liquid in kg/m3, g = 9.8 N/kg, and Δh the change in depth in metres. The total pressure also includes the atmospheric pressure pressing on the surface (about 1.0 × 105 Pa).

✏️Worked example

A diver swims 25 m below the surface of the sea. The density of sea water is 1030 kg/m3. (a) EXTENDED Calculate the pressure due to the water at this depth. [2] (b) Atmospheric pressure is 1.0 × 105 Pa. Calculate the total pressure on the diver. [1] (c) The glass of her mask has an area of 0.018 m2. Calculate the force of the water on it. [2]

(a) \( \Delta p = \rho g \Delta h = 1030 \times 9.8 \times 25 = 252\,350 \) Pa = 2.5 × 105 Pa.

(b) 2.52 × 105 + 1.0 × 105 = 3.5 × 105 Pa.

(c) F = pA = 3.52 × 105 × 0.018 = 6300 N (using the total pressure; 4500 N from the water alone).

Check it. Every 10 m of water adds about one atmosphere (105 Pa), so 25 m adds about 2.5 atmospheres. It agrees.
Using the diver’s mass or area in Δp = ρgΔh. The pressure at a depth depends only on the depth, the liquid’s density and g — not on the object there.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Theory.) A student of weight 610 N stands on the floor. His shoes touch the floor over an area of 420 cm2. Calculate the pressure on the floor, with the unit. [3] (Modelled on 0625/42 June 2026 Q4(b)(iii).)
p = F/A = 610 / 420 = 1.5 N/cm2 (1.45), or 1.5 × 104 Pa using 0.042 m2.
2. (Theory.) A block of ice weighs 650 N and measures 0.80 m × 0.40 m × 0.25 m. Calculate the greatest pressure it can exert on the ground. [3] (Modelled on 0625/32 June 2026 Q2(b).)
Greatest pressure on the smallest face: 0.40 × 0.25 = 0.10 m2; p = 650 / 0.10 = 6500 Pa.
3. (Multiple choice.) EXTENDED A submarine is 400 m below the surface of the sea. Apart from g, which quantities determine the pressure on it due to the water? A: depth and the submarine’s surface area. B: depth and the density of the water. C: depth, density and the submarine’s mass. D: density and the submarine’s volume.
B. Δp = ρgΔh.
4. (Theory.) Explain why a sharp knife cuts more easily than a blunt one. [2]
The sharp edge has a much smaller area in contact, so the same force produces a much larger pressure on the food.
5. (Theory.) A water tank is 2.5 m deep. EXTENDED Calculate the pressure due to the water at the bottom (density 1000 kg/m3). [2]
Δp = 1000 × 9.8 × 2.5 = 24 500 Pa (2.5 × 104 Pa).
6. (Theory.) Explain why a dam is built much thicker at the bottom than at the top. [2]
The pressure of the water increases with depth, so the force on each square metre of the dam is greatest at the bottom; the wall must be strongest there.
7. (Multiple choice.) Which is a unit of pressure? A: N m. B: N/m2. C: N/kg. D: kg/m3.
B (the pascal).

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Under Pressure” — pressure in liquids of different densities
  • BBC Bitesize — pressure in solids and liquids