Engineering Mechanics II Problem Set 3 2022 REVISION PAPER

Engineering Mechanics II Problem Set 3 Solutions are provided on a separate paper b) Denoting the height of the gap between the two cylinder bottoms by H, derive an ex­ pression for the depth of water in the outer cylinder, h, for H h0 (assume the free surface to be horizontal). c) Derive an expression for Vi, the horizontal velocity in the radial direction averaged over the gap height, H, at the outflow from under the inner cylinder, i.e., Vi at r = di/2. d) How does the gap-averaged radial velocity, V (r), vary with r for 0 ≤ r ≤ di/2? e) Assume that Vi and V (r) are known and that the pressure at the outflow corner of the inner cylinder, r = di/2, is pi = ρg(h H). Obtain an expression for p(r) as a function of the known values. For this part, you can neglect the pressure variation with z in the gap between the two cylinder bottoms and any effects of unsteadiness. f) ) With what vertical force is the inner cylinder being pushed downwards? Neglect the inner cylinder’s weight.