Consider the system shown in Figure 1. Figure 1 Interconnected Tanks The two reservoirs have the same (constant) cross sectional areas and the flow rates through the two valves are described by the orifice equation: = 2 (1) Where is the density of the fluid. a) Write the conservation of mass for Tank 1 using the pressure 1 as the state, and and 1 as the inputs. b) Write the conservation of mass for Tank 2 using the pressure 2 as the state, and 1 and 2 as the inputs. c) Now, combine the two equations you wrote in (a) and (b) with equation (1) and manipulate the resulting system to show that it can be written as: 1 = 1(1, 2, ) 2 = 2(1, 2) Where is the only input to the system, and 1 2,p p are the two states. Note: I am not requiring you to do this for this problem but the following is an additional part of the problem that could be asked for. d) Assume that the system is operating around a constant equilibrium condition: 1() = 1,0 1() 2() = 2,0 2() () = ,0 ()