A cylindrical vessel of diameter D drains through an orifice of diameter DO at the bottom of the vessel. The pressure in the vessel is maintained at atmospheric pressure. Derive an expression for the height of the liquid in the vessel as a function of time, and state your simplifying assumptions. Use the expression you derived to calculate the time at which the height reaches half of its original value or 0.25 m. Also find the height when the time is 20 s. For the second part use the following data: D=5 cm, DO=5 mm, initial height h0=0.5 m