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Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of salt is dissolved and T2 containing 50 gallons of pure water. A brine solution containing 2 pounds of salt per gallon is pumped from outside into T1 at a rate of 4 gal/min and salt solution is circulated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 is withdrawn out of the system at the same rate as the brine solution from outside into T1 (i.e., 4 gal/min), and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1 and T2 respectively using the Laplace transform method for nonhomogeneous systems of ODES. Determine the time it would take for the salt contents in the two tanks to be equal.

Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of salt is dissolved and T2 containing 50 gallons of pure water. A brine solution containing 2 pounds of salt per gallon is pumped from outside into T1 at a rate of 4 gal/min and salt solution is circulated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 is withdrawn out of the system at the same rate as the brine solution from outside into T1 (i.e., 4 gal/min), and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1 and T2 respectively using the Laplace transform method for nonhomogeneous systems of ODES. Determine the time it would take for the salt contents in the two tanks to be equal.

Advanced Engineering Mathematics
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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4. Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of salt is dissolved and T2 containing 50 gallons of pure water. A brine solution containing 2 pounds of salt per gallon is pumped from outside into T1 at a rate of 4 gal/min and salt solution is circulated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 is withdrawn out of the system at the same rate as the brine solution from outside into T1 (i.e., 4 gal/min), and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1 and T2 respectively using the Laplace transform method for nonhomogeneous systems of ODES. Determine the time it would take for the salt contents in the two tanks to be equal.
Transcribed Image Text:4. Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of salt is dissolved and T2 containing 50 gallons of pure water. A brine solution containing 2 pounds of salt per gallon is pumped from outside into T1 at a rate of 4 gal/min and salt solution is circulated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 is withdrawn out of the system at the same rate as the brine solution from outside into T1 (i.e., 4 gal/min), and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1 and T2 respectively using the Laplace transform method for nonhomogeneous systems of ODES. Determine the time it would take for the salt contents in the two tanks to be equal.
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