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The flow system shown in the figure is activated at time t = 0. Let Q. (t) denote the amount of solute present in the ith tank at time t. Assume that all the flow rates are a constant 10L/min It follows that the volume of solution in each tank remains constant; assume this volume to be 1000L The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.7 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 perfectly. Tank 1 Tank 2 a. Set up a system of first-order differential equations that models this situation. Q{ Q2 b. If Q; (0) = 20 kg and Q2(0) = 0 kg, find the amount of solute in each tank after t minutes. Qı(t) = kg Q2(t) = kg

The flow system shown in the figure is activated at time t = 0. Let Q. (t) denote the amount of solute present in the ith tank at time t. Assume that all the flow rates are a constant 10L/min It follows that the volume of solution in each tank remains constant; assume this volume to be 1000L The concentration of solute in the inflow to Tank 1 (from a source other than Tank 2) is 0.7 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 perfectly. Tank 1 Tank 2 a. Set up a system of first-order differential equations that models this situation. Q{ Q2 b. If Q; (0) = 20 kg and Q2(0) = 0 kg, find the amount of solute in each tank after t minutes. Qı(t) = kg Q2(t) = kg

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The flow system shown in the figure is activated at time t = 0. Let Q:(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 0.7 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 perfectly. Tank 1 Tank 2 a. Set up a system of first-order differential equations that models this situation. Q1 Q2 b. If Q1 (0) = 20 kg and Q2 (0) = 0 kg. find the amount of solute in each tank after t minutes. Q1 (t) = kg Q2(t) = kg C. As t → 00, how much solute is in each tank? In the long run, Tank 1 will have kg of solute. In the long run, Tank 2 will have kg of solute. (Reread the question and think about why this answer makes sense.)
Transcribed Image Text:The flow system shown in the figure is activated at time t = 0. Let Q:(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 0.7 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 perfectly. Tank 1 Tank 2 a. Set up a system of first-order differential equations that models this situation. Q1 Q2 b. If Q1 (0) = 20 kg and Q2 (0) = 0 kg. find the amount of solute in each tank after t minutes. Q1 (t) = kg Q2(t) = kg C. As t → 00, how much solute is in each tank? In the long run, Tank 1 will have kg of solute. In the long run, Tank 2 will have kg of solute. (Reread the question and think about why this answer makes sense.)
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