Floating cube expression

A.)See attachment, it shows a cube floating in a fluid. Derive an expression relating the submerged depth X, the specific weight of the cube, and the specific weight of the fluid. b.)See attachment: If the cylinder, made of a uniform material is placed in fresh water @ 95 degrees Celsius, how much of it's height would be above the surface (ignore kerosene note and 600mm note - refers to another problem) I used the specific weight of water @ 9.44 kN/m^3

Tank pressures and U-tube

A.) See attachment - Amounts from left to right, top to bottom are: 500mm, 460mm, S.G.=0.8, S.G.=1.05, 300mm, 300mm and Tank X is water. *Calculate difference in pressure between centers of tank X and Y. B.) See attachment - Amounts are: Pa=2.7kPa, 0.05m, 20mm, S.G.(Oil)=0.6, S.G.=1.4, 30mm, 10mm. *Find the distance d for the U tube.

Manometers

2.) See attachment: Two water manometers are connected to a tank of air. One leg of the manometer is open to 100kPa absolute pressure while the other leg is subjected to 90kPa. Find the difference in deflection between both manometers, delta ha - delta hb. 3.) See attachment: The inclined differential manometer shown in the figure contains carbon tetrachloride. Initially the pressure differential between pipes A and B, which contains a brine with specific gravity=1.1, is zero as illustrated in the figure. It is desired that the manometer give a differential reading of 12in.(measured along the inclined tube) for a pressure differential of 0.1 psi. Determine the angle of inclination.

Bouyancy, Closed Vessel, Mass

A.) See attachment: Metal part, 2, is attached by a thin cord from a floating wood block, 1. The wood block has a specific gravity(S.G.)=0.3 and dimensions of 50x50x10mm. The metal part has a volume of 6600mm^3. Find mass, m2, of metal part and the tension, T, in the cord. B.) See attachment: The closed vessel has water of air pressure 10psi at the surface. One side of the vessel has a spout that is closed by a 6 inch diameter circular gate that is hinged along one side as illustrated. The horizontal axis of the hinge is located 10 feet below the water surface. Determine the minimum torque that must be applied at the hinge to hold the gate closed. Neglect the weight of the gate and... click for more

Water Tanks

A.) A water tank with a homogenous rectangular gate in one side as in the attachment. The gate, weighing 200#, pivots about a horizontal axis located 10 ft below the water surface. If the gate can only open inwardly, what will be the reaction of the gate (in direction perpendicular to the gate) against the bottom of the tank opening? The width of the gate is 2 ft, and the friction at the axis is negligible. B.) Water enters a cylindrical tank through two pipes at rates of 250 and 100 gal/min. If the level in the tank remains constant, calculate the average velocity of the flow leaving the tank through an 8 inch inside diameter pipe.