4. Consider two tanks T1 and T2 with T1 containing 50 gallons of water in which 25 pounds of saltis dissolved and T2 containing 50 gallons of pure water. A brine solution containing 2 poundsof salt per gallon is pumped from outside into T1 at a rate of 4 gal/min and salt solution iscirculated at rates of 6 gal/min from T1 to T2 and 2 gal/min from T2 to T1. If the content of T2 iswithdrawn out of the system at the same rate as the brine solution from outside into T1 (i.e., 4gal/min), and the mixture in each tank is well mixed, find the salt contents y1 (t) and y2 (t) in T1and T2 respectively using the Laplace transform method for nonhomogeneous systems ofODES. Determine the time it would take for the salt contents in the two tanks to be equal.

We are given the following. Consider two tanks T1 and T2 with T1 containing 50 gallons of water in…

Answered: Consider two tanks T1 and T2 with T1…

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 connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time.(b) Give an initial-value problem that governs the amount (grams) of salt in eachtank as a function of time.(c) Give the interval of definition for the solution of this initial-value problem.
The brine solution is recycled using a series of mixing tanks before being released outside of the tanks. Tank A receives pure water at a rate of 4 L/min. The solution is pumped to Tanks B and C at rates of 2 L/min and x L/min, respectively, from Tank A, which originally contains 500 L of brine solution in which 200 g of salt is first dissolved. At a rate of 4 L/min, Tank B from its original 400 L of brine solution in which 1000 g of salt has been dissolved pumps the solution to Tank C. At a rate of y L/min, Tank C, which originally holds 400 L of pure water, pumps the solution back to Tank B. Meanwhile, Tank C releases z L/min of solution out of the system. a. Determine the values of x, y, and z if the volume of the solution within each tank stays constant throughout time. b. Find out the brine solution's concentration coming out of each tank at time t-8 minutes. 2 L/min TANK B TANKA 4 L/min y L/min Pure water @4 L/min x L/min TANK C z L/min
Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows from lake A into lake B, and from lake B into lake C, both inflows and outflows at the same rate of 525 km3/year. Suppose that at time t=0 (years), the pollutant concentration of lake B, caused by past industrial pollution that has now been ordered to cease, is five times that of lake A. If the outflow from lake B to lake C is perfectly mixed lake water, how long will it take to reduce the pollution concentration in lake B to twice that of lake A? Choose all correct answers. B Approximately 6.3 years. Approximately 4.4 years. Approximately 5 years. Approximately 8.3 years. Approximately 7 years.
A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine solution containing 0.5 kg/liter of salt flows into the container at a rate of 1 liter/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 0.5 liters/min. How much salt is in the container after 10 minutes? When the tank is about to overflow, another drain is opened at 1 liter/min. How much salt is in the tank when the volume returns to what it was initially?
A 200-liter tank initially contains 100 liters of brine solution containing 25kg of salt. A brine solution containing 0.5 kg/ liter of salt flows into the container at a rate of 1 liter/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 0.5 liters/min. How much salt is in the container after 10 minutes? When the tank is about to overflow, another drain is opened at 1 liter/min. How much salt is in the tank when the volume returns to what it was initially?
My cat Pythagoras has purchased and installed in my back yard a large barrel with a 400-gallon capacity. It is initially half full of clean water. But he has three hoses feeding this barrel, each with a rate of flow of 2 gal./min. of water. Two provide the barrel with clean water, but the third contains a concentration of 2 g/gal. of liquid calculus text books. My other cat, Jolie, has decided to sabotage this process by puncturing a hole toward the bottom of this barrel that allows 4 gal./min. to leak. If we assume that there is a benevolent feline deity that blissfully stirs this barrel with a rather large spoon, then write a differential equation that mathematically models the rate at which the amount of liquid calculus text books changes in the barrel (at least up to the time it fills). Thereafter, solve this differential equation.
A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the upper tap that feeds the water tank with a constant speed of v1 liters per minute and the lower tap that expels the water from the tank with a constant speed of v2 liters per minute . Suppose that v1 = 11 liters / minute and v2 = 3 liters / minute. If the tank has a capacity of 75 liters, when will the tank be filled?
A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially contains 100 liters of pure water. The mixed solution is drained at 3 liters per minute. At what time will the solution contain 10% ammonia?

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