Water is flowing into the top of an open cylindrical tank (diameter $D$ ) at a volume flow rate of $Q_{i}$ and out of a hole in the bottom at a rate of $Q_{o}$. The tank is made of wood that is very porous, and the water is leaking out through the wall uniformly at a rate of $q$ per unit of wetted surface area. The initial depth of water in the tank is $z_{1}$. Derive an equation for the depth of water in the tank as a function of time. If $Q_{i}=10 \mathrm{gpm}, Q_{o}=5 \mathrm{gpm}, D=5 \mathrm{ft}, q=0.1 \mathrm{gpm} / \mathrm{ft}^{2}$, and $z_{1}=3 \mathrm{ft}$, is the level in the tank rising or falling?