The flow system shown in the figure is activated at time t = 0. Let Q₁ (t) denote the amount of solute present in the th 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. a. Set up a system of first-order differential equations that models this situation. [3]. b. If Q₁ (0) = 20 kg and Q₂ (0) = 0 kg, find the amount of solute in each tank after Q₁ (t) = Q₂ (t) = c. As t→ ∞o, how much solute is in each tank? In the long run, Tank 1 will have Q₁ 22 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.) minutes. kg kg Tank 1 Tank 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The flow system shown in the figure is activated at time t = 0. Let Q₁ (t) denote the amount of solute present in the th 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.
a. Set up a system of first-order differential equations that models this situation.
2₁
Q₂
b. If Q₁ (0) = 20 kg and Q₂ (0) = 0 kg, find the amount of solute in each tank after
Q₁ (t) =
Q₂ (t) =
c. As t → ∞o, how much solute is in each tank?
In the long run, Tank 1 will have
Q₁
22
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.)
minutes.
kg
kg
Tank 1
Tank 2
Transcribed Image Text:The flow system shown in the figure is activated at time t = 0. Let Q₁ (t) denote the amount of solute present in the th 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. a. Set up a system of first-order differential equations that models this situation. 2₁ Q₂ b. If Q₁ (0) = 20 kg and Q₂ (0) = 0 kg, find the amount of solute in each tank after Q₁ (t) = Q₂ (t) = c. As t → ∞o, how much solute is in each tank? In the long run, Tank 1 will have Q₁ 22 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.) minutes. kg kg Tank 1 Tank 2
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