4. Suppose a heated open-air tank is fed a salt solution with concentration 3 lb/galvia pipe at a rate of 3gal/min. Water in the tank evaporates at rate of 2gal/min anda fresh water is added at a rate 3gal/min. The well-mixed solution is drained at arate of 4gal/min. If the tank initially contains a volume of 400gals with 100 lb ofsalt. Solve for the amount of salt in the tank after 100 min. Also find the limitingamount of salt in the tank after a long time.

First one must model the problem through an Initial Value Problem.

Answered: 4. Suppose a heated open-air tank is…

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 tanks are interconnected. Tank A contains 70 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 20 liters of water. A solution of 4 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 1 grams/L flows into Tank B at a rate of 10 L/min. The tanks are well mixed. The tanks are connected, so 6 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks. dx dt dy dt x (0) = 11 2 y(0) =
Suppose a water tank is being pumped out at 3 L/min. The water tank starts at 10 L of clean water. Water with toxic substance is flowing into the tank at 2 L/min, with concentration 20t g/L at time t. When the tank is half empty, how many grams of toxic substance are in the tank (assuming perfect mixing)?
2) A tank, which has a capacity of 100 L, is initially half full of a solution that contains 50g of chemical. A solution containing 0.5g/L of the same chemical flows into the tank at a rate of 6L/min, and the well-stirred mixture flows out at a rate of 4 L/min. Determine the concentration of chemical in the tank just before the solution overflows.
4. A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
3) Problem: A large tank holds 300 gallons of brine solution with 40 pounds (Ib) of salt. A concentration of 2 lb/gallon is pumped in a rate of 4 gal/min. The concentration leaving the tank is pumped out at a rate of 3 gal/min. How much salt is in the tank after 12 minutes?
2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?

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