Pressure at Depth — Swimming Pool (Worked Example)

Given

• h = 3.0 m

• ρ = 1000 kg/m³

• g = 9.8 m/s²

• P₀ = 101,325 Pa

Find

The absolute pressure P.

Principle

Hydrostatic pressure adds ρgh to atmospheric pressure: P = P₀ + ρgh.

Formula

Solution

1. Write the formula: $P = P_0 + \rho g h$

2. Substitute: $P = 101325 + (1000)(9.8)(3.0)$

3. Gauge part: $29{,}400\ \mathrm{Pa}$

4. Add: $P = 101325 + 29400 = 130{,}725\ \mathrm{Pa}$

Unit check

kg/m³ × m/s² × m = N/m² = Pa — correct.

What this means physically

≈131 kPa — about 1.29 atmospheres. Your ears feel the extra 29 kPa; that is why they pop when you dive to the deep end.