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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If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C. The specific heat capacity is
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) =
35. A tank contains 10 lb of salt dissolved in 30 gal of water. Suppose 2 gal of brine containing 1 lb of dis- solved salt per gallon runs into the tank every minute and that the mixture (kept uniform by stirring) runs out at the same rate. a. Find the amount of salt in the tank at time t. b. How long does it take (to the nearest second) for the tank to contain 15 lb of salt?
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)?
A device used for treating of agri-effluents has an inflow of 8 cubic feet per second and the amount of phosphorous in it is 20 milligrams per liter. The device media consists of wood and charcoal. This device eliminates 0.8 milligrams per liter of phosphorous for every 1 cubic feet of media. If the device is required to have an outflow phosphorous concentration of 0.9 milligrams per liter then find the volume of the filter media required for the device.
Need help. Show complete and thorough solution with good explanation.
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.
A tank contains 1000L of pure water. Brine that contains 0.02kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.07kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t) = ... 2. How much salt is in the tank after 5 hours? Answer (in kilograms):
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?
0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L Pure Water with 5 kg pollutant Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. What is the final equation of yA(t)? What is the final equation of yB(t)?
solve and draw a diagram of the problem Two large tanks, each holding 100L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3L/min and from tank B into tank A at a rate of 1L/min. The liquid inside each tank is kept well stirred. Pure water flows into tank A at a rate of 6L/min. The solution flows out of the system from tank A at 4L/min and from tank B at 2L/min. If, initially, tank A contains pure water and tank B contains 20kg of salt, determine the mass of salt in each tank at time t ≥ 0.

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