Solutions to homework 2

MAE 308 HW2 SolutionsAssigned Jan 28, 2013Due: Feb 3, 2013P1. All fluids in the figure are at 20ºC. If atmosphere pressure=101.33 kPa and the bottompressure is 242 kPa absolute, what is the specific gravity of fluid X?(Note at this temperature the specific weight for SAE 30 oilis 8720 N/m 3 , water 9790 N/m 3 , and mercury 133100 N/m 3 .)P2. Determine ΔP between points A and B. The specific weights for fluids are as follows:

P3. In the attached figure, both the tank and the slanted tube are open to the atmosphere. IfL=2.13m, what is the angle of tilt ϕ of the tube.P4. Gate AB in the figure is 1.2 m long and 0.8 m into the paper. Neglecting atmosphericpressure effects, compute the force F on the gate and its center of pressure position X.Solutions: The centroidal depth of the gate is

P5. Gate ABC in the figure has a fixed hinge at B and is 2 m wide into the paper. If the waterlevel is high enough, the gate will open. Compute the depth h for which this happens.P6. A block of wood (SG=0.6) floats in fluid X in the figure such that 75% of its volume issubmerged in fluid X. Estimate the gage pressure of the air in the tank.

P7. The tank of liquid in the figure accelerates to the right with the fluid in rigid-body motion.(a) Compute a x in m/s2; (b) Why doesn’t the solution to part (a) depend on fluid density? (c)Compute gage pressure at point A if the fluid density is 1260 kg/m 3 .(c) For glycerol, the density is 1260 kg/m 3 . There are two ways to calculate P A :