2. (10 points) Consider the following interacting system, where valve equations show that the flows between the two tanks depend on the levels in both tanks, each affecting the other. A recycle process to the first tank has been added. Figure 2: Cascade tanks with recycle. a) Write the unsteady-state mass balances of the whole process, given that fi(t)[ft3/min] and f2(t)[ft3/min] are step inputs with known magnitudes and known density . b) Linearize the the unsteady-state mass balance equations around the equilibrium points (h10,h20). c) Draw a block diagram with appropriate transfer functions representative of the given process. 2. (10 points) Consider the following interacting system, where valve equations show that the flows between the two tanks depend on the levels in both tanks, each affecting the other. A recycle process to the first tank has been added. Figure 2: Cascade tanks with recycle. a) Write the unsteady-state mass balances of the whole process, given that fi(t)[ft3/min] and f2(t)[ft3/min] are step inputs with known magnitudes and known density . b) Linearize the the unsteady-state mass balance equations around the equilibrium points (h10,h20). c) Draw a block diagram with appropriate transfer functions representative of the given process