Problem-

Given: A cube whose sides are length L. The cube is open at the top (exposed to an atmospheric pressure, P_O), but all of the side and bottom faces are solid material. The cube is completely filled with a fluid. There is no motion in the cube.

A: Prove that the force exerted on any side face is greater if the cube is filled with water than if the cube is filled with air.

B: If L = 3 feet and the temperature of the fluid is 70°F, calculate the pressure at the bottom of the cube for each fluid, in atmospheres of pressure. The density of water is 62.4 lb/ft³. Gravity is 32.174 ft/S². The Universal Gas constant is: R = 0.7302 (atm-ft³)/(lbmole-°R)

C: If the cube is located on the International Space Station and an external pressure, P_O is applied to the open face of the cube (i.e. P_O ≠  0), prove whether the proof in Part A is still valid.

Additional information-

The problem belongs to Mechanical Engineering and the problem is about a cube filled with fluid at an atmospheric pressure PO. Problems such as, if the cube is filled with water what would be the force exerted. If the fluid is 70°F, the pressure exerted at the bottom of the cube and if the cube is located on International Space Station and an external pressure is applied etc are solved in the solution in detailed calculations.