Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20litres of water and 40 grams of salt, and Tank X contains 20 litres of fresh water.Additionally, fresh water enters Tank Y at a rate of 4 litres/min, and the well-stirredsolution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a differentconnecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min,of which some flows back into Tank Y at a rate of 4 litres/min, while the remainderleaves the system.(a)Draw a diagram that depicts the flow process described above. Let Qx(t) andQy(1), respectively, be the amount of salt in each tank at time t. Write downdifferential equations and initial conditions for Qx and Qy that model theflow process.(b)Is the system of differential equations homogeneous? Justify your answer.(c)Use the Laplace transform to find the amount of salt in each tank at ume r.(d)After 10 minutes, Tank X develops a leak and additional mixtures leaves outthe tank at 0.05 litre/min. Rework the system with differential equations inpart (a) for t> 10. (You are not required to solve the system).

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Answered: Consider two interconnected tanks of…

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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