The diagram below illustrates a system of two interconnected tanks, A and B.3 L/mA4 L/m12 L/m5 gm/L10 gm/LVol = 100 LitersVol = 100 Liters3 L/m4 L/m12 L/mAt time t=0, both tanks contain 100 liters of pure water.• At that time, saline solution with a concentration of 10 gm/L (of salt) begins toflow into tank A at a rate of 4 L/min, and saline solution with a concentration of 5gm/L begins to flow into tank B at a rate of 12 L/min.• Solution flows from tankA to tank B at a rate of 3 L/min, and flows back from tankB to tank A at the same rate.• Solution flows out of tank A at a rate of 4 L/min and out of tank B at a rate of 12L/min.• The solutions in both tanks are mixed rapidly, and you may assume that theconcentration in both tanks is uniform at all times.(a)Find the functions Qa(t) and QB(t) which give the quantities of salt (in grams)at time t in tanks A and B respectively.(b)Find the limiting quantities of salt in both tanks as t goes to infinity, orexplain why no such limiting quantities exist.

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Answered: he diagram below illustrates a system…

he diagram below illustrates a system of two interconnected tanks, A and B. 3 L/m A B 4 L/m 12 L/m 5 gm/L 10 gm/L Vol = 100 Liters Vol = 100 Liters %3D 3 L/m 4 L/m 12 L/m

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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Question

The diagram below illustrates a system of two interconnected tanks, A and B.
3 L/m
A
4 L/m
12 L/m
5 gm/L
10 gm/L
Vol = 100 Liters
Vol = 100 Liters
3 L/m
4 L/m
12 L/m
At time t=0, both tanks contain 100 liters of pure water.
• At that time, saline solution with a concentration of 10 gm/L (of salt) begins to
flow into tank A at a rate of 4 L/min, and saline solution with a concentration of 5
gm/L begins to flow into tank B at a rate of 12 L/min.
• Solution flows from tankA to tank B at a rate of 3 L/min, and flows back from tank
B to tank A at the same rate.
• Solution flows out of tank A at a rate of 4 L/min and out of tank B at a rate of 12
L/min.
• The solutions in both tanks are mixed rapidly, and you may assume that the
concentration in both tanks is uniform at all times.
(a)
Find the functions Qa(t) and QB(t) which give the quantities of salt (in grams)
at time t in tanks A and B respectively.
(b)
Find the limiting quantities of salt in both tanks as t goes to infinity, or
explain why no such limiting quantities exist.

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