The flow system shown in the figure is activated at time t== 0. Let Q.(t) denote the amount of solute present in the i th tank at time f. Assume that all the flow rates are a constant 1O 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 0.6 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. a. Set up a system of first-order differential equations that models this situation. -1/50 1/100 1/100 -1/50 Q2 b. If Q, (0) = 20 kg and Q2(0) = 0 kg, find the amount of solute in each tank after t minutes. %3D Q,() = kg kg Q2) = C. As t- oo, how much solute is in each tank? 400 ka of solute.
The flow system shown in the figure is activated at time t== 0. Let Q.(t) denote the amount of solute present in the i th tank at time f. Assume that all the flow rates are a constant 1O 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 0.6 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. a. Set up a system of first-order differential equations that models this situation. -1/50 1/100 1/100 -1/50 Q2 b. If Q, (0) = 20 kg and Q2(0) = 0 kg, find the amount of solute in each tank after t minutes. %3D Q,() = kg kg Q2) = C. As t- oo, how much solute is in each tank? 400 ka of solute.
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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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 i th tank at time f.
Assume that all the flow rates are a constant 1O 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 0.6 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.
a. Set up a system of first-order differential equations that models this situation.
-1/50
1/100
1/100
-1/50
b. If Q, (0) = 20 kg and Q2(0) = 0 kg, find the amount of solute in each tank after t minutes.
%3D
0,() =
kg
kg
Q2) =
C. As t+ oo, how much solute is in each tank?
kg of solute.
In the long run, Tank 1 will have 400
kg of solute.
In the long run, Tank 2 will have 200
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