Recall and use the equation for the change in pressure beneath the surface of a liquid Δp = ρ g Δh

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – Pressure

1.8 Pressure

Learning Objective

Recall and use the equation for the change in pressure beneath the surface of a liquid \$\Delta p = \rho g \Delta h\$

Key Concepts

  • Pressure definition: \$p = \frac{F}{A}\$

  • Units: Pascal (Pa) = N·m⁻²

  • Atmospheric pressure: \$1 \text{ atm} = 101\,325 \text{ Pa}\$

  • Hydrostatic pressure: pressure increase with depth in a fluid.

Derivation of the Hydrostatic Pressure Formula

Consider a horizontal slab of fluid at depth \$h\$ with thickness \$\Delta h\$.

  1. Weight of the slab: \$W = \rho \, A \, \Delta h \, g\$ where \$A\$ is the area.

  2. Pressure difference between the top and bottom of the slab: \$\Delta p = \frac{W}{A} = \rho g \Delta h\$.

Variables

SymbolQuantityUnits
\$\Delta p\$Change in pressurePa (N·m⁻²)
\$\rho\$Density of the liquidkg·m⁻³
\$g\$Acceleration due to gravity9.81 m·s⁻² (≈10 m·s⁻² for exam)
\$\Delta h\$Depth differencem

Typical Densities of Common Liquids

LiquidDensity \$\rho\$ (kg·m⁻³)
Water (4 °C)1000
Sea water1025
Oil (vegetable)≈ 920
Mercury13 600

Worked Example

Problem: Calculate the pressure increase at a depth of \$5.0\ \text{m}\$ in fresh water.

Given: \$\rho = 1000\ \text{kg·m}^{-3}\$, \$g = 9.81\ \text{m·s}^{-2}\$, \$\Delta h = 5.0\ \text{m}\$.

Solution:

\$\Delta p = \rho g \Delta h = (1000)(9.81)(5.0) = 49\,050\ \text{Pa} \approx 4.9\times10^{4}\ \text{Pa}\$

The pressure increase is about \$0.49\ \text{atm}\$ (since \$1\ \text{atm}=101\,325\ \text{Pa}\$).

Practice Questions

  1. What is the pressure increase at a depth of \$2.0\ \text{m}\$ in oil with \$\rho = 920\ \text{kg·m}^{-3}\$? Use \$g = 10\ \text{m·s}^{-2}\$ for simplicity.

  2. A diver is \$12\ \text{m}\$ below the surface of sea water. Calculate the absolute pressure on the diver’s suit if atmospheric pressure is \$1.0\ \text{atm}\$. (Take \$\rho_{\text{sea}} = 1025\ \text{kg·m}^{-3}\$, \$g = 9.8\ \text{m·s}^{-2}\$.)

  3. Explain why a dam must be built thicker at the base than at the top, using the hydrostatic pressure equation.

Common Mistakes to Avoid

  • Forgetting to convert depth to metres if given in centimetres.

  • Using the wrong value of \$g\$; the exam often allows \$g = 10\ \text{m·s}^{-2}\$ for quick calculations.

  • Confusing pressure increase \$\Delta p\$ with absolute pressure \$p{\text{abs}} = p{\text{atm}} + \Delta p\$.

  • Omitting units in the final answer.

Suggested diagram: A vertical column of liquid showing depth \$h\$, pressure \$p\$ at the surface, and \$p + \Delta p\$ at depth \$h + \Delta h\$.

Summary Checklist

  • Know the definition \$p = F/A\$ and the unit Pascal.

  • Remember the hydrostatic pressure formula \$\Delta p = \rho g \Delta h\$.

  • Identify each variable and its typical units.

  • Be able to substitute values and calculate \$\Delta p\$ quickly.

  • Convert \$\Delta p\$ to atmospheres or other convenient units when required.