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# Find the force $P$ required to hold the gate in the position shown in Fig. The gate is $5 \mathrm{~m}$ wide.

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In solving problems involving forces on curved surfaces, the free-body diagram of the curved surface and the fluid directly above it must be first identified. For this problem, we will isolate the gate and the water above it, then identify the forces acting on it. The water on the left portion exerts a hydrostatic force $F_1$ towards the water on the curved surface. There is also a hinge in the gate which will have the reaction forces $F_x$ and $F_y$. The weight of the water $F_w$ above the gate must be included too. The last force acting on the gate is external force $P$ required to hold the gate. Now, our free-body diagram is complete and it is shown below. ## Recommended textbook solutions #### Fundamentals of Electric Circuits

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