(a) Write the differential equation for the height h during the emptying of the funnel.

(b) Integrate the above differential equation to find an expression for the time required to empty the

funnel from an initial height ho. Explain the dependence of the emptying time on he

(c) Compared to a cylindrical tank that has a constant cross-section area = n(h/4² along its height, will

the time to emptying for the above tank be faster or slower - explain (you can answer this qualitatively,

without having to work out the emptying time for the constant area tank in detail).

(d) Now, consider a situation where the top of the funnel is closed and the headspace above the water

level in the funnel is maintained at a constant gage pressure Ap above atmospheric pressure. Write the

modified differential equation for the height h in this case (no need to solve the differential equation,

just set it up).