A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, is proportional to the liquid level to the 1.5 power; that is, w = Rh15 where R is a constant. If a single stream enters the tank with flow rate wi, find the transfer function H'(s)!W'(s). Identify the gain and all time constants. Verify units. The cross-sectional area of the tank is A. Density p is constant.

Problem 4.8A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, is 1.5proportional to the liquid level to the 1.5 power; that is, w = Rh where R is a constant. If asingle stream enters the tank with flow rate wi, find the transfer function H'(s)/W'(s). Identifythe gain and all time constants. Verify units. The cross-sectional area of the tank is A.Density p is constant. Step-by-step solution Step 1 of 9 ^Refer to Figure E4.8 from the textbook.Consider the given equation, 1.5 w = Rh ………(1)Where,Outflow rate is represented as w,Constant is represented as R, andHeight of the tank is represented as h.From the figure, the mass balance equation is, d(Ah) = w i w ……….(2) dtWhere,Density is represented as ,Flow rate is represented as w and iCross-sectional area of the tank is represented as A.