The cross section of a rectangular AB of width 2.5 m hinged along A is shown in the figure below. The weight of the gate is 55 kg, and it is used to retain the water at depth 3.3m. Calculate the minimum force R at B to hold the gate.

A semi-circular vertical plate is partially submerged in the water as shown in the figure. What is the force on the plate due to hydrostatic pressure if the water level is 1 meter from the top of the plate. Set up the integral only.

Rectangle Gate AB has length L and width b into the paper is hinged at B and has negligible weight. The liquid level, water, h does not reach the top of the gate for an angle theta. Find an equation for the force P, required to keep the gate in equilibrium. Solve for width, b. In the figure. (hint: draw a free-body diagram for the left and right side of the gate separately)

A long solid cylinder of radius 0.8 m hinged at point A is used as an automatic gate, When the water level reaches 5 m, the gate opens by turning about the hinge at point A. Determine (a) the hydrostatic force acting on the cylinder and its line of action when the gate opens and (b) the weight of the cylinder per m length of the cylinder.