Q2 (6') A surge tank, as shown in the figure below, is often designed with a slotted weir such that the outlet flow rate, w, is proportional to the liquid level (h) to the 1.5 power, that is, w = Rh1.5 where R is a fixed constant. As seen in the figure, if a single stream enters the tank with a flow rate wi, which changes over time during the operation. H'(s) (a) Find the transfer function W/(s) (b) Identify the steady state gain and the time constant of the transfer function in part (a). Weir 1 h 20 Hint: Mass balance will be used to derive the dynamic model of level with respect to the changes in inlet flow W over time and assume the cross-sectional area of the tank is A, and the density (2) is constant