A vertical rectangular wall of width 2.0 m retains water to a depth of 3.0 m. The upper edge of the wetted portion is at the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², what is the torque of the hydrostatic force about the horizontal line passing through the upper edge of the wetted surface?
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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 portion is at the free surface. Taking ρ = 1000 kg/m³ and g = 10 m/s², what is the torque of the hydrostatic force about the horizontal line passing through the upper edge of the wetted surface?

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G1 Physics · Accepted Answer

At depth y, P = ρgy. For a horizontal strip of width b and thickness dy, dF = ρgby dy. The torque of this force about the upper edge is dτ = y dF = ρgby²dy. Integrating from 0 to h, τ = ρgb ∫₀ʰ y²dy = ρgbh³/3. Substitute ρ = 1000 kg/m³, g = 10 m/s², b = 2.0 m, h = 3.0 m. Therefore, τ = 1000×10×2×3³/3 = 180000 N·m = 180 kN·m. Correct option: D.