Question

(2 points) The flow system shown in the figure is activated at time t 0. Let Qi(t) denote the amount of solute present in the ith tank at time t Assume that all the flow rates are a constant 10 L./min. It follows that the volume of solution in each tank remains constant; assume this volume to be 1000 L. The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.8 kg/L, and the concentration of solute in the inflow to Tank 2 (from a source other than Tank 1) is 0 kg/L. Assume each tank is mixed perfectily a. Set up a system of first-order differential equations that models this situation. ei Q1 1/100 1/100 Q2 b. If Q1(0) Q1(t) 0 kg and Q2(0) 20 kg, find the amount of solute in each tank aftert minutes kg Q2(t) kg c. As t00, how much solute is in each tank? In the long run, Tank 1 will have 400/3 In the long run, Tank 2 will have 200/3 (Reread the question and think about why this answer makes sense.) kg of solute kg of solute

Answer 1

"Given data According to the given question, the given information Let us consider Q_1(t) and Q_2(t) are denote the amount at present in, solute in the inflow Tank 1. Tank 1 = 0.8 kg/L Tank 2 = 0 kg/L The given system (a) [Q_1^' Q_2^'] = [-1/50 1/100 1/100 -1/50] [Q_1 Q_2] + [2 0] Then A = [-1/50 1/100 1/100 -1/50] E(0) = [2 0] the characteristic equation