A surge tank (shown below) is designed with a slotted weir so that the outflow mass flow rate w is related to the liquid level h to the 1.5 power; that is: w=Rh1.5 where R is a constant. A single stream enters the tank with mass flow rate wi. The crosssectional area of the tank is A, and the liquid density is , both are constant. Figure E4.8 a. Derive a dynamic model for this system. b. Linearize the dynamic model. c. Find the transfer function Wi(s)H(s) and determine the process gain and time constants. Hint: Put the transfer function into first-order form