Two very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure. 1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively. 2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t». 3. Explain why this relationship makes intuitive sense. 4. Use this relationship to help find the amount of salt in tank B at t = 30 min.
Two very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure. 1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively. 2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t». 3. Explain why this relationship makes intuitive sense. 4. Use this relationship to help find the amount of salt in tank B at t = 30 min.
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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Two very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure.
1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively.
2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t».
3. Explain why this relationship makes intuitive sense.
4. Use this relationship to help find the amount of salt in tank B at t = 30 min.
Transcribed Image Text:A
100 gal
mix
3 gal/min
mix
2 gal/min
B
100 gal
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