(20 pts) 3. A perfect stirred tank has two input streams and one outlet stream, all consisting of the same liquid as shown in the following figure. In the figure, F1, F2, F3 denote volumetric flow rates (m/s), 11, 12, Tz denote temperatures (K), h is the level (m), and A is the cross-sectional area of the tank (m). T.FI TF TT A We also have the following information and assumptions: The outlet flow rate = kV with k a known constant parameter The liquid has a constant density p (kg/m2) The liquid has a constant specific heat capacity Cp (J/(kg) When calculating enthalpy, consider Tres OK (10 pts) (a) Derive a dynamic model that will describe the transient operation of the tank. (5 pts) (b) Make a degrees of freedom analysis assuming that both streams 1 and 2 come from upstream units (i.e., their flow rates and temperatures are known functions of time). (5 pts) (c) What are the input variables and output variables of the model derived in part (a)