The cylinder gate of Fig 2.80 is made from a circular cylinder and a plate hinge
ID: 1828701 • Letter: T
Question
The cylinder gate of Fig 2.80 is made from a circular cylinder and a plate hinged at the dam. The gate position is controlled by pumping water into or out of the cylinder. The center of gravity of the empty gate is on the line of symmetry 4 ft from the hinge. It is at equilibrium when it is empty in the position shown. How many cubic feet of water must be added per foot of cylinder to hold the gate in its position when the water surface is raised 3 ft?
Please provide a step-by-step solution (the final answer is 17.27 ft^3). Thanks!!
The cylinder gate of Fig 2.80 is made from a circular cylinder and a plate hinged at the dam. The gate position is controlled by pumping water into or out of the cylinder. The center of gravity of the empty gate is on the line of symmetry 4 ft from the hinge. It is at equilibrium when it is empty in the position shown. How many cubic feet of water must be added per foot of cylinder to hold the gate in its position when the water surface is raised 3 ft?Explanation / Answer
if the water is raised by 3 ft the pressure increases by rho *3ft*g;
so total force also increases by =projected area * rho*3ft*g = 3.14*9*3*32.174 *1.94 = 5291.76lbft/s^2;
to counter act the force the equal amintu of weight is added so volume of water added =
V*rho *32.174 =5291.76 =>V = 84.7 ft^3
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