A tank contains water initially at a depth of $3 \mathrm{ft}$. The water flows out of a hole in the bottom of the tank, and air at a constant pressure of $10 \mathrm{psig}$ is admitted to the top of the tank. If the water flow rate is directly proportional to the square root of the gage pressure inside the bottom of the tank, derive expressions for the water mass flow rate and air mass flow rate as a function of time. Be sure to define all symbols you use in your equations.