Two square gates close two openings in a conduit connected to an open tank of wa

Question

Two square gates close two openings in a conduit connected to an open tank of water as shown in the figure. When the water depth, h, reaches 5 m it is desired that both gates open at the same time. Determine the weight of the homogeneous horizontal gate and the horizontal force, R, acting on the vertical gate that is required to keep the gates closed until this depth is reached. The weight of the vertical gate is negligible, and both gates are hinged at one end as shown. Friction in the hinges is negligible.

Explanation / Answer

Consider the torque around the hinge in horizontal gate T(weight)=2W (weight acts in the centre of the plate) Pressure due to water at the gate=pg(5-3) This force also acts in the centre of the gate. 2W=1000*10*2*16*2 W=320000 N For vertical gate T net due to pressure around the hinge =integral of (pgh*4*(9-h)) from 5 to 9. T net=2026666.66 R*4 =2026666.66 R=506666.66 N

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