A reservoir is filled with water of density ρ. The depth of the water is ℎ. A gate is used to block the water on the right side as shown in the figure. The gate is hinged at the free surface level (z = 0), and a cable is attached to the gate ℎ/2 above the hinge. Compute how much pulling force F is needed to keep the gate closed. The atmospheric pressure is a constant p=p0 in case needed. The width (horizontal length) of the gate is W.

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 rectangular gate of width "a", length "b" and inclined at an angle "A", with water on one side is shown in the figure. Use a=9.5 ft, b=5ft, z=6.5ft and angle A=55 degrees. (a) Determine the location of the center of the gate from the water surface along the plane of the gate (in feet). (b) Determine the eccentricity (in feet). (c) Determine the location of the center of pressure from the water surface along the plane of the gate (in feet). (d) Determine the vertical distance (in feet) of the center of the gate from the water surface. (e) Determine the total resultant force (in lb) acting on the side of the gate.

As shown in the figure, a sluice gate with a width of 1 m is supported by hinge A (the sluice gate BC is integral). Find the force, F, that must be applied to B to keep the gate from opening. However, the fluid is water and the thickness and weight of the gate are ignored.