A vertical rectangular gate of width 1.5 m retains oil of density 800 kg/m³ up to a depth of 2.0 m. The upper edge of the gate coincides with the free surface. Taking g = 10 m/s², the resultant hydrostatic force on the gate is N × 10³ N. Find N.
Physics · Fluid Mechanics · question based on variation of pressure
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Question

A vertical rectangular gate of width 1.5 m retains oil of density 800 kg/m³ up to a depth of 2.0 m. The upper edge of the gate coincides with the free surface. Taking g = 10 m/s², the resultant hydrostatic force on the gate is N × 10³ N. Find N.

Physics · Fluid Mechanics · question based on variation of pressure

G1 Physics · Accepted Answer

For a vertical rectangular surface with its upper edge at the free surface, F = ρgbh²/2. Substitute ρ = 800 kg/m³, g = 10 m/s², b = 1.5 m, h = 2.0 m. Therefore, F = 800×10×1.5×2²/2 = 24000 N = 24×10³ N. Hence, N = 24.