KinexiaLEARN PHYSICS

Fluid Pressure — Scuba Diver at 15 m (Worked Example)

Easy
Problem

A scuba diver swims 15 m below the surface of the ocean (seawater ρ = 1025 kg/m³). What is (a) the gauge pressure and (b) the absolute pressure at that depth? (P_atm = 101325 Pa.)

Given

  • h = 15 m

  • ρ = 1025 kg/m³

  • g = 9.81 m/s²

  • P_atm = 101325 Pa

Find

Gauge pressure P_gauge and absolute pressure P_abs.

Principle

Hydrostatic pressure grows linearly with depth: each meter of water adds ρg of pressure on top of the atmosphere.

Formula

Solution

  1. Gauge: Pgauge=1025×9.81×15P_{gauge} = 1025 \times 9.81 \times 15

  2. Calculate: Pgauge=150,829 Pa≈1.51×105 PaP_{gauge} = 150{,}829\ \mathrm{Pa} \approx 1.51 \times 10^5\ \mathrm{Pa}

  3. Absolute: Pabs=101,325+150,829=252,154 PaP_{abs} = 101{,}325 + 150{,}829 = 252{,}154\ \mathrm{Pa}

P_gauge ≈ 1.51 × 10⁵ Pa; P_abs ≈ 2.52 × 10⁵ Pa (≈ 2.49 atm)

Unit check

(kg/m³)(m/s²)(m) = kg/(m·s²) = Pa. Correct.

What this means physically

The water alone adds about 1.5 atmospheres — your body feels 2.5 atm total. That is why divers' air consumption rises with depth and why ascending too fast is dangerous: dissolved gases expand as pressure falls.

Common mistake

Reporting only ρgh as 'the pressure' when absolute was asked — or vice versa. Gauge ignores the atmosphere; absolute includes it.