Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 4 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank A at 5 L/min and from tank B at 3 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time t20. 8 L/min 0.2 kg/L 5 L/min A x(t) 100 L x(0) = 0 kg 4 L/min 1 L/min What is the solution to the system? B y(t) 100 L y(0) = 20 kg 3 L/min Q 4
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 4 L/min and from B into A at a rate of 1 L/min. The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the system from tank A at 5 L/min and from tank B at 3 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time t20. 8 L/min 0.2 kg/L 5 L/min A x(t) 100 L x(0) = 0 kg 4 L/min 1 L/min What is the solution to the system? B y(t) 100 L y(0) = 20 kg 3 L/min Q 4
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 large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 4 L/min and from B into A at a rate of 1 L/min.
The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 8 L/min. The (diluted) solution flows out of the
system from tank A at 5 L/min and from tank B at 3 L/min. If initially, tank A contains pure water and tank B contains 20 kg of salt, determine the mass of salt in each tank at time
t≥0.
Q
Q
x(t) =
8 L/min
0.2 kg/L-
y(t) =
5 L/min
A
x(t)
100 L
x(0) = 0 kg
4 L/min
What is the solution to the system?
A
1 L/min
B
y(t)
100 L
y(0) 20 kg
3 L/min
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VIEWStep 2: Frame the equation on rate of salt in each tank.
VIEWStep 3: Eigen value of the coefficient matrix
VIEWStep 4: Eigenvector of the corresponding eigenvalue:
VIEWStep 5: Complementary solution to the differential equations:
VIEWStep 6: Particular solution to the differential equations:
VIEWStep 7: Solution to the initial value problem
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