= 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 0.6 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. 2-882-8 b. If Q1(0) = 20 kg and Q2(0) = 10 kg, find the amount of solute in each tank after t minutes. Q1(t) = Q2(t) = kg kg Tank 1 Tank 2 (Hint: You need to find the general homogeneous solution and also guess a particular solution, just as we did for single equations. Try guessing x(t) where C and D are constants.) = [២]. c. As t∞, 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.)
= 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 0.6 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. 2-882-8 b. If Q1(0) = 20 kg and Q2(0) = 10 kg, find the amount of solute in each tank after t minutes. Q1(t) = Q2(t) = kg kg Tank 1 Tank 2 (Hint: You need to find the general homogeneous solution and also guess a particular solution, just as we did for single equations. Try guessing x(t) where C and D are constants.) = [២]. c. As t∞, 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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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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 0.6 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.
2-882-8
b. If Q1(0) = 20 kg and Q2(0) = 10 kg, find the amount of solute in each tank after t minutes.
Q1(t) =
Q2(t) =
kg
kg
Tank 1
Tank 2
(Hint: You need to find the general homogeneous solution and also guess a particular solution, just as we did for single equations. Try
guessing x(t)
where C and D are constants.)
=
[២].
c. As t∞, 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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64e88f82-8895-4781-bbe1-865f339a6888%2Fcced36a8-113e-4183-a5a9-6d8d410da3d0%2Fdk4i7vj_processed.png&w=3840&q=75)
Transcribed Image Text:=
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 0.6 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.
2-882-8
b. If Q1(0) = 20 kg and Q2(0) = 10 kg, find the amount of solute in each tank after t minutes.
Q1(t) =
Q2(t) =
kg
kg
Tank 1
Tank 2
(Hint: You need to find the general homogeneous solution and also guess a particular solution, just as we did for single equations. Try
guessing x(t)
where C and D are constants.)
=
[២].
c. As t∞, 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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