Two mixing tanks are setup as follows: Tank 1 contains 150 gallons of water with 7 pounds of salt dissolved in it and Tank 2 contains 100 gallons of pure water. A solution with 4 pounds per gallon flows into Tank 1 at a rate of 2 gallons per minute. The well mixed solution in Tank 1 flows into Tank 2 at a rate of 2 gallons per minute, and drains from Tank 1 at a rate of 3 gallons per minute. A solution with 6 pounds per gallon flows into Tank 2 at a rate of 1 gallons per minute. The well mixed solution in Tank 2 flows into Tank 1 at a rate of 3 gallons per minute. Let Q₁(t) be the amount of salt (in pounds) in Tank 1 at time t. Let Q₂(t) be the amount of salt (in pounds) in Tank 2 at time t. Lett be time in minutes. Write a system of linear differential equations for these tanks in matrix form where Q = With the inital condition: The equilibirum solution to this differential equation is: Q + 3-18 181 -18 2(0) =
Two mixing tanks are setup as follows: Tank 1 contains 150 gallons of water with 7 pounds of salt dissolved in it and Tank 2 contains 100 gallons of pure water. A solution with 4 pounds per gallon flows into Tank 1 at a rate of 2 gallons per minute. The well mixed solution in Tank 1 flows into Tank 2 at a rate of 2 gallons per minute, and drains from Tank 1 at a rate of 3 gallons per minute. A solution with 6 pounds per gallon flows into Tank 2 at a rate of 1 gallons per minute. The well mixed solution in Tank 2 flows into Tank 1 at a rate of 3 gallons per minute. Let Q₁(t) be the amount of salt (in pounds) in Tank 1 at time t. Let Q₂(t) be the amount of salt (in pounds) in Tank 2 at time t. Lett be time in minutes. Write a system of linear differential equations for these tanks in matrix form where Q = With the inital condition: The equilibirum solution to this differential equation is: Q + 3-18 181 -18 2(0) =
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 mixing tanks are setup as follows:
Tank 1 contains 150 gallons of water with 7 pounds of salt dissolved in it and Tank 2 contains 100 gallons of pure water. A solution with 4 pounds per gallon flows
into Tank 1 at a rate of 2 gallons per minute. The well mixed solution in Tank 1 flows into Tank 2 at a rate of 2 gallons per minute, and drains from Tank 1 at a rate of
3 gallons per minute. A solution with 6 pounds per gallon flows into Tank 2 at a rate of 1 gallons per minute. The well mixed solution in Tank 2 flows into Tank 1 at a
rate of 3 gallons per minute.
Let Q₁(t) be the amount of salt (in pounds) in Tank 1 at time t.
Let Q₂ (t) be the amount of salt (in pounds) in Tank 2 at time t.
Lett be time in minutes.
Write a system of linear differential equations for these tanks in matrix form where Q
Q₁
Q2
With the inital condition:
The equilibirum solution to this differential equation is:
Q' =
Q(0)
Q
=
Q +
181
18
18
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