Q1: The space between two 15 cm long concentric cylinders is filled with glycerine (viscosity 0.5 N.s/m2), figure 1. The inner cylinder has a radius R = 7 cm and the gap width between the cylinders a =b= 0.25 cm, Determine the torque and the power required to rotate the inner cylinder at ω=180 rev/min. The outer cylinder is fixed. Assume the velocity distribution in the gap to be linear.
Q2: The rigid gate OAB of figure 2 is hinged at O and rests against a rigid support at B. What minimum horizontal force, P, is required to hold the gate closed if its width is 3 m? Neglect the weight of the gate and friction in the hinge. The back of the gate is exposed to the atmosphere.
Q3: Water at 20˚ C is flowing in the pipe and out to the atmosphere as in figure 3. If friction can be neglected, calculate the flow rate.
Note that the elevation given in the figure is in meters and the Mercury (Hg) have specific gravity of 13.55.