[Solved] : Sketch shows two cylindrical tanks interconnected

The sketch shows two cylindrical tanks interconnected with a pipe which has a valve that creates a constant resistance to flow of R_f when fully open. The height of liquid (of density ) in the first tank is h_in and the second tank h_out. The cross-sectional area of the first tank is A_in m² and the second tank A_out m². The flow rate through of liquid through the valve is given by Where: Q = flow rate in m³ s^-1 P_in = pressure due to height of liquid in first tank (P_a) P_out = pressure due to height of liquid in second tank (P_a) a) Produce a mathematical model of the process to determine the change in height of fluid in the second tank when the valve is open. b) Determine the time constant for the system.