Two tanks are connected as in Figure 1.6. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into tank 2 at the rate of 5 gallons per minute, and tank 2 also has an output of 5 gallons per minute. Deter- mine the amount of salt in each tank at any time. Also, determine when the concentration of salt in tank 2 is a minimum and how much salt is in the tank at that time. Hint: Solve for the amount of salt in tank 1 at time t and use this solution to help determine the amount in tank 2. 5 gal/min: 1/2 Ib'gal 5 gal'min Tank 1 Tank 2 5 gal'min
Two tanks are connected as in Figure 1.6. Tank 1 initially contains 20 pounds of salt dissolved in 100 gallons of brine. Tank 2 initially contains 150 gallons of brine in which 90 pounds of salt are dissolved. At time zero, a brine solution containing 1/2 pound of salt per gallon is added to tank 1 at the rate of 5 gallons per minute. Tank 1 has an output that discharges brine into tank 2 at the rate of 5 gallons per minute, and tank 2 also has an output of 5 gallons per minute. Deter- mine the amount of salt in each tank at any time. Also, determine when the concentration of salt in tank 2 is a minimum and how much salt is in the tank at that time. Hint: Solve for the amount of salt in tank 1 at time t and use this solution to help determine the amount in tank 2. 5 gal/min: 1/2 Ib'gal 5 gal'min Tank 1 Tank 2 5 gal'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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Transcribed Image Text:Two tanks are connected as in Figure 1.6. Tank 1
initially contains 20 pounds of salt dissolved in 100
gallons of brine. Tank 2 initially contains 150 gallons
of brine in which 90 pounds of salt are dissolved. At
time zero, a brine solution containing 1/2 pound of
salt per gallon is added to tank 1 at the rate of 5 gallons
per minute. Tank 1 has an output that discharges brine
into tank 2 at the rate of 5 gallons per minute, and tank
2 also has an output of 5 gallons per minute. Deter-
mine the amount of salt in each tank at any time. Also,
determine when the concentration of salt in tank 2 is a
minimum and how much salt is in the tank at that time.
Hint: Solve for the amount of salt in tank 1 at time t
and use this solution to help determine the amount in
tank 2.
5 gal/min: 1/2 Ib'gal
5 gal'min
Tank 1
Tank 2
5 gal'min
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