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

1.8 Pressure

Objective

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

What is Pressure?

Pressure is the force applied per unit area. Think of it like the push you feel when you press your palm against a wall. The deeper you go under water, the more “push” you feel because the water above is heavier. 📏

Key Equation

The change in pressure with depth is given by:

\$\Delta p = \rho g \Delta h\$

  • ρ (rho) – Density of the liquid (kg m⁻³)

  • g – Acceleration due to gravity (≈9.8 m s⁻²)

  • Δh – Change in depth (m)

Units & Symbols

SymbolUnitExample
ρkg m⁻³1000 (water)
gm s⁻²9.8
Δhm5
ΔpPa (N m⁻²)49000

Analogy: The Slinky in a Bottle

Imagine a slinky inside a bottle. When you push the top of the slinky down, the bottom feels a stronger push because the slinky above is heavier. Similarly, the deeper you go in a liquid, the more weight of liquid sits above you, increasing pressure. 🎈

Example Problem

  1. Water depth: Δh = 5 m

  2. Density of water: ρ = 1000 kg m⁻³

  3. Gravity: g = 9.8 m s⁻²

  4. Calculate Δp.

Using the formula:

\$\Delta p = 1000 \times 9.8 \times 5 = 49\,000 \text{ Pa}\$

So at 5 m depth, the pressure is 49 kPa higher than at the surface. 🚤

Quick Quiz

  • What happens to Δp if you double the depth Δh? 🤔

  • How would the pressure change if you used a liquid with half the density of water? 💧

  • Calculate the pressure increase at 10 m depth in seawater (ρ ≈ 1025 kg m⁻³). 📐