KinexiaLEARN PHYSICS

Pressure at Depth — Dam Base (Worked Example)

Easy
Problem

A dam holds back water 50 m deep at its base. What is the absolute water pressure there? (ρ = 1000 kg/m³, g = 9.8 m/s²)

Given

  • h = 50 m

  • ρ = 1000 kg/m³

  • g = 9.8 m/s²

  • P₀ = 101,325 Pa

Find

The absolute pressure P.

Principle

Dams are thickest at the base because pressure grows linearly with depth: P = P₀ + ρgh.

Formula

Solution

  1. Substitute: P=101325+(1000)(9.8)(50)P = 101325 + (1000)(9.8)(50)

  2. Gauge part: 490,000 Pa490{,}000\ \mathrm{Pa}

  3. Add: P=591,325 PaP = 591{,}325\ \mathrm{Pa}

591,325 Pa (≈ 591 kPa)

Unit check

kg/m³ × m/s² × m = N/m² = Pa. The ρgh term is a pressure, matching P₀ — consistent.

What this means physically

≈591 kPa — nearly 6 atmospheres. This is why dam walls slope outward toward the base: they must resist pressure that grows with every metre of depth.

Common mistake

Thinking pressure depends on the reservoir's total volume. Only depth matters — a narrow pipe 50 m tall gives the same pressure (hydrostatic paradox).