Two tanks are interconnected as illustrated below: Tank 1 2 C. min min. Tank 2 Suppose that Tank 1 contains 1 gallon of brine in which 4 pounds of salt are initially dissolved, and Tank 2 initially contains 1 gallon of pure water. At time t = 0, the mixtures are pumped between the two tanks, each at a rate of 2 gal/min. Assume the mixtures are well stirred. Let x₁ (t) and x₂ (t) be the amount of salt (in pounds) in Tank 1 and Tank 2, respectively, at time t. a. Formulate the system of linear differential equations that describes the amount of salt in the tanks. b. Obtain the initial-value problem above in the matrix form X' : = AX. Examine the solution of the system in part (b) for x₁ and x₂. d. Compute the amount of salt in each tank after 45 seconds.
Two tanks are interconnected as illustrated below: Tank 1 2 C. min min. Tank 2 Suppose that Tank 1 contains 1 gallon of brine in which 4 pounds of salt are initially dissolved, and Tank 2 initially contains 1 gallon of pure water. At time t = 0, the mixtures are pumped between the two tanks, each at a rate of 2 gal/min. Assume the mixtures are well stirred. Let x₁ (t) and x₂ (t) be the amount of salt (in pounds) in Tank 1 and Tank 2, respectively, at time t. a. Formulate the system of linear differential equations that describes the amount of salt in the tanks. b. Obtain the initial-value problem above in the matrix form X' : = AX. Examine the solution of the system in part (b) for x₁ and x₂. d. Compute the amount of salt in each tank after 45 seconds.
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:Two tanks are interconnected as illustrated below:
Tank 1
2
2
min
gal
min
Tank 2
Suppose that Tank 1 contains 1 gallon of brine in which 4 pounds of salt are initially dissolved,
and Tank 2 initially contains 1 gallon of pure water. At time t = 0, the mixtures are pumped
between the two tanks, each at a rate of 2 gal/min. Assume the mixtures are well stirred. Let
x₁ (t) and x₂ (t) be the amount of salt (in pounds) in Tank 1 and Tank 2, respectively, at time
t.
a. Formulate the system of linear differential equations that describes the amount of salt in
the tanks.
b. Obtain the initial-value problem above in the matrix form X' = AX.
c. Examine the solution of the system in part (b) for x₁ and x₂.
d. Compute the amount of salt in each tank after 45 seconds.
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