0 Sta) [6 Marks] The capacitance of an open vessel is where p + pa is the pressure at the base of the vessel, 1: is the volume of liquid within the vessel and pa is the atmospheric pressure. Consider the system shown in Figure 9. It consists of a conical vessel with a restriction at its outlet. lMater flows into it at the rate w,;(t). To simplify the equations, assume that the vessel is a perfect cone (Le. that it narrows to a radius of l] at its base}. The ow rate through the restriction is we = WI: - pa. i. Derive a formula for the capacitance of the vessel. [3 marks] ii. Find a nonlinear state-variable model for the system. [3 marks]