2. Consider a mixing system consists of two tanks. Tank 1 is filled with 200 litres of water initially containing 0.04 kg of salt dissolved in it and Tank 2 contains 200 litres of fresh water. Fresh water enters Tank 1 at a rate of 4 litres/hour. Through a connecting pipe water flows from Tank 2 into Tank 1 at a rate of 4 litres/hour. Through a different connecting pipe 8 litres/hour of water flows out of Tank 1 into Tank 2. Tank 2 contains one outlet where the solution is drained at the rate of 4 litres/hour. c) Use Laplace transform to find the equation indicating the amount of salt in Tank 1 at time t.
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Let Y(t) be the amount of salt in Tank 2 at time t. Show more…
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Consider a closed system of three well-mixed brine tanks. Tank 1 has a volume of 20 gallons, tank 2 has a volume of 15 gallons, and tank 3 has a volume of 4 gallons. Mixed brine flows from tank 1 to tank 2, from tank 2 to tank 3, and from tank 3 back to tank 1. The flow rate between each pair of tanks is 60 gallons per minute. At time zero, tank 1 contains 28 lb of salt, tank 2 contains 11 lb of salt, and tank 3 contains no salt. Solve for the amount (lb) of salt in each tank at time t (minutes). Also determine the limiting amount (as t approaches infinity) of salt in each tank. (Solve the problem by using Laplace Transform)
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Problem 1 (Cascading tanks). Consider the following system of two tanks: Tank A Tank B At t = 0, Tank A contains 100 gallons of a salt solution with concentration 0.5 lb/gal, and Tank B initially contains 100 gallons of pure water. Fresh water is poured into Tank A at a rate of 4 gal/min, and the resulting solution flows from Tank A to Tank B at a rate of 6 gal/min. Part of the solution contained in Tank B then flows back into Tank A at a rate of 2 gal/min, while the rest flows out of Tank B at a rate of 4 gal/min. (a) Write down a system of differential equations, together with an initial condition, that describes the amount of salt in each of the tanks. (b) Solve the system from part (a). (c) Describe the behavior of the salt content in each tank as t → ∞.
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