## Description

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 ρ) in the first tank is h_{in} and the second tank h_{out}. The cross-sectional area of the first tank is A_{in }m^{2} and the second tank A_{out} m^{2}. The flow rate through of liquid through the valve is given by Where: Q = flow rate in m^{3} 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.