A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m, with the upper edge of the wetted part at the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², the hydrostatic torque about the upper edge is N kN·m. Find N.
Physics · Fluid Mechanics · question based on variation of pressure
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Question

A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m, with the upper edge of the wetted part at the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², the hydrostatic torque about the upper edge is N kN·m. Find N.

Physics · Fluid Mechanics · question based on variation of pressure

G1 Physics · Accepted Answer

At depth y, P = ρgy. For a horizontal strip, dF = ρgby dy. Its torque about the upper edge is dτ = y dF = ρgby²dy. Therefore, τ = ρgb ∫₀ʰ y²dy = ρgbh³/3. Substitute ρ = 1000, g = 10, b = 2, h = 3. Thus, τ = 1000×10×2×27/3 = 180000 N·m = 180 kN·m. Hence, N = 180.