What is hydrostatic pressure? Derive an expression for the pressure at a depth h below the free surface of a liquid. Why are dam walls thicker at the base?

1. 1 · Define hydrostatic pressure. It is the thrust per unit area exerted by a fluid at rest. SI unit: pascal (N m⁻²).
2. 2 · Draw the figure. A liquid with an imaginary upright cylinder of area A and height h, its top face at the surface. Mark P₂ on top and P₁ at the bottom.
3. 3 · Write the forces. Upward force P₁A, downward force P₂A, and the weight of the liquid ρAhg.
4. 4 · Balance them. At rest: P₁A − P₂A − ρghA = 0, so P₁ − P₂ = ρgh.
5. 5 · Put the top at the surface. P₂ = Patm, so P = Patm + ρgh. The area cancels, so the shape of the vessel does not matter.
6. 6 · Real life. Pressure is greatest at the bottom of a dam, so the wall is built thickest there.
7. 7 · Close in one line. Liquid pressure rises in a straight line with depth and with density.

Scoring tip: Write 'the area A cancels' in words. It earns the mark for 'pressure does not depend on the shape of the vessel'.