Two square gates close two openings in a conduit connected to an open tank of water as s...

Two square gates close two openings in a conduit connected to an open tank of water as shown in Fig. P2.47. 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.