Problem $4$:

A cylindrical tank which has a diameter $D$ is supplied with an incompressible oil of density $$ by a pipe which has a diameter of $d$ and an associated velocity $U.$ The oil is leaving the tank through two other pipes, one of which is horizontal and has a diameter of $d_h=\frac{4}{5}d$ and another is vertical with a diameter of $d_v=\frac{3}{2}d.$ The velocities associated with the horizontal and vertical pipes are $U_h=\frac{1}{4}U$ and $U_v=\frac{2}{5}U,$ respectively. Find the rate at which the water level is changing, $\frac{dh}{dt},$ as a function of the variables $U,d,$ and $D.$ Is the tank filling or emptying?