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Extended · Practice questions · Pressure in liquids

Down where it’s heavy.

Six original Cambridge-style questions on calculating pressure with depth, the role of density, why shape does not matter, and rearranging for depth.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Depth and density

Δp = ρgΔh.

01
[2 marks]

Write the equation for the change in pressure with depth in a liquid, and state what each symbol represents.

  • Δp = ρgΔh. ✓
  • ρ = density (kg/m³), g = gravitational field strength (N/kg), Δh = depth below the surface (m). ✓
02
Calculation
[2 marks]

Calculate the pressure due to the water at a depth of 5.0 m in a lake. Take the density of water as 1000 kg/m³ and g = 10 N/kg.

Δp = ρgΔh = 1000 × 10 × 5.0

50000 Pa

03
Calculation
[2 marks]

A tank holds oil of density 850 kg/m³. Calculate the pressure due to the oil at a depth of 3.0 m, using g = 9.8 N/kg.

Δp = 850 × 9.8 × 3.0

24990 Pa (about 25 kPa)

04
Analysis
[3 marks]

The wall of a dam is built much thicker at the bottom than at the top. Explain why, in terms of pressure.

  • Pressure increases with depth, since Δp = ρgΔh. ✓
  • So the water pushes hardest near the bottom of the dam. ✓
  • The wall is made thicker there to withstand the greater pressure and force. ✓
05
Analysis
[2 marks]

Two differently shaped containers, one narrow and one wide, are filled with the same liquid to the same depth. Compare the pressure at the base of each and explain your answer.

  • The pressure at the base is the same in both. ✓
  • Pressure depends only on depth and density (Δp = ρgΔh), not on the shape or width of the container. ✓
06
Calculation
[3 marks]

The pressure due to the water at a certain depth in a reservoir is 39200 Pa. Taking the density of water as 1000 kg/m³ and g = 9.8 N/kg, calculate the depth.

Δh = Δp ÷ (ρg) = 39200 ÷ (1000 × 9.8) Δh = 39200 ÷ 9800

Δh = 4.0 m

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