A tank is being emptied as shown below.

a$.$ Derive an equation for the change in the height of the water in the tank, $h,$ with respect to time. Neglect viscosity and assume that $D_t{D}_{\text{o}\text{u}\text{t}}.$

b$.$ How long would it take for the tank to drain if the initial height was $6$ feet, $D_t=5ft$ and $D_{\text{o}\text{u}\text{t}}=2$ inches. $($Ans: $8\mathrm{.}36$ min $,$ I think $(3)$

c$.$ What term in your differential equation could you easily change to account for viscous effects? How would you do that?

d$.$ Write a new differential equation $($but do not solve it$),$ if the top of the tank was closed and pressurized above atmospheric pressure.