The upper edge of a gate in a dam runs along the water surface. The gate is 2 m high and 4m wide and is hinged along the horizontal line through its top. Find the torque due to the force from water.
Text Solution
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A
Consider a strip of (4m × dy) at a height y.
Force on the strip
dF = ρ ρ g (2 - y)4dy;
Torque d τ τ = ρ ρ g (2 - y) 2 4 dy
τ τ = ρ ρ g4 
= 10 3 × 10 × 4 
= 10.67 × 10 4 N – m.
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