October/12/2016
Maximum Points: 400 points
Please read: All problems have equal points. Problem 3 may be the most
straightforward. Problem 1 is the shortest. Problem 4 is similar to an assignment
question but a bit more involved. Problem 2 may be a bit tricky.
Hydrostatics
1. A force, F is applied on a semi-cylinder of length, L and radius, R such that it is
completely submerged (see Figure below). The density of liquid and solid is $p$
and $\rho_s$, respectively. Using the elemental area as shown calculate the following:
a. The total force, dF on the elemental area in terms of $\theta$, R, L and g.
b. Calculate the elemental force in the z-direction, $dF_z$.
c. Calculate the force, F needed to keep the body submerged as shown.
d. Calculate the buoyancy force, $F_b$ and compare it to F.
Points: 25+35+20+20=100