please show step by step

For each question, show the steps for linearizing the dynamic balance, taking the Laplace transform of the linearized balance in deviation variables, and rearranging the transfer function to standard form. 1. A surge tank with a valve on the exit is shown below. The exit flowrate is proportional to the square root of the liquid level in the tank (q-Ch"), where is the valve constant The process is running at steady state, with an inlet flowrate (q) of 20 m/min. The cross sectional area of the tank is 2 mand the valve constant (C) is 5 m/min a. Write the dynamic balance for the tank. Use this balance to write the transfer function H'(s)Q/'(s) in terms of the process variables. b. What is the gain and time constant of this transfer function (with units)? Answer: K-1.6 min/m; tau - 3.2 min c. If the inlet flowrate is reduced to 15 m/min, what is the final height of fluid in the tank? Determine this value from the linearized transfer function in part a. Answer: h - 8 m