The sketch shows two cylindrical tanks interconnected with a pipe which has a valve that creates a constant resistance to flow of Rf when fully open. The height of liquid (of density ρ) in the first tank is hin and the second tank hout. The cross-sectional area of the first tank is Ain m2 and the second tank Aout m2. The flow rate through of liquid through the valve is given by Where: Q = flow rate in m3 s-1 Pin = pressure due to height of liquid in first tank (Pa) Pout = pressure due to height of liquid in second tank (Pa) 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.