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Question

The upper edge of a gate in a dam runs along the water surface. The gate is 2 m high and 4 m wide and is hinged along the horizontal line through its top. Find the torque( in kN~m) due to the force from water about the top edge of the gate.

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Solution

Consider a strip of thickness dy at a height y from bottom of the gate.
Area of this strip is 4 dy
Force on the strip
dF=ρg(2y)4dy;
Torque due to this force about top edge of the plate is
dτ=4ρg(2y)2dy
τ=ρg4[4y+y332y2]20
=103×10×4[8+838]
=10.67×104 N-m.

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