A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m. The upper edge of the wetted part coincides with the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², what is the resultant hydrostatic force on the wall?
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Question

A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m. The upper edge of the wetted part coincides with the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², what is the resultant hydrostatic force on the wall?

Options

G1 Physics · Accepted Answer

At depth y below the free surface, P = ρgy. For a horizontal strip of width b and thickness dy, dF = P b dy = ρgby dy. Integrating from y = 0 to y = h, F = ρgb ∫₀ʰ y dy = ρgbh²/2. Substitute ρ = 1000 kg/m³, g = 10 m/s², b = 2.0 m, h = 3.0 m. Therefore, F = 1000×10×2×3²/2 = 90000 N = 90 kN. Correct option: C.