Consider the two tanks given in the figure below. 10 Vmin of pure water 5 lmin TankA Tank B 500 I 1000I 0% of Salt 90% of Salt 15 Vmin 10 Vmin of Salt Solution There are two tanks which has a mixture of Water and Salt. Total volume of the mixture of Tank A is 500 liter and the volume of Tank B is 1000 liter. The initial concentration of Salt for Tank A is 0% (it means that pure Water). The initial concentration of Salt for Tank B is 90%. There is an outlet for Tank A through which the solution is going out at the rate of 15 liter/min. There are two outlets for Tank B and the solution is going out at the rate of 5 liter/min through one outlet and the solution is going out at the rate of 10 liter/min through the other outlet. There are two inlets for Tank A. Pure water is coming in at the rate of 10 liter/min through one inlet and solution is coming in at the rate of 5 liter/min with the yet unknown concentration through one inlet. There is one inlet for Tank B. A solution is coming in at the rate of 15 liter/min with the yet unknown concentration through the inlet. What will be the amount of salt at any given time in the tanks? (Note: Show the fundamental matrix. Show your results as x(t) for tank A and y(t) for tank B.)

Consider the two tanks given in the figure below. 10 Vmin of pure water 5 lmin TankA Tank B 500 I 1000I 0% of Salt 90% of Salt 15 Vmin 10 Vmin of Salt Solution There are two tanks which has a mixture of Water and Salt. Total volume of the mixture of Tank A is 500 liter and the volume of Tank B is 1000 liter. The initial concentration of Salt for Tank A is 0% (it means that pure Water). The initial concentration of Salt for Tank B is 90%. There is an outlet for Tank A through which the solution is going out at the rate of 15 liter/min. There are two outlets for Tank B and the solution is going out at the rate of 5 liter/min through one outlet and the solution is going out at the rate of 10 liter/min through the other outlet. There are two inlets for Tank A. Pure water is coming in at the rate of 10 liter/min through one inlet and solution is coming in at the rate of 5 liter/min with the yet unknown concentration through one inlet. There is one inlet for Tank B. A solution is coming in at the rate of 15 liter/min with the yet unknown concentration through the inlet. What will be the amount of salt at any given time in the tanks? (Note: Show the fundamental matrix. Show your results as x(t) for tank A and y(t) for tank B.)

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Consider the two tanks given in the figure below.
10 lmin of pure
water
5 /min
TankA
Tank B
500 I
1000I
0% of Salt
90% of Salt
15 l/min
10 /min of Salt
Solution
There are two tanks which has a mixture of Water and Salt. Total volume of the mixture of Tank A is
500 liter and the volume of Tank B is 1000 liter. The initial concentration of Salt for Tank A is 0% (it means
that pure Water). The initial concentration of Salt for Tank B is 90%. There is an outlet for Tank A through
which the solution is going out at the rate of 15 liter/min. There are two outlets for Tank B and the solution is
going out at the rate of 5 liter/min through one outlet and the solution is going out at the rate of 10 liter/min
through the other outlet. There are two inlets for Tank A. Pure water is coming in at the rate of 10 liter/min
through one inlet and solution is coming in at the rate of 5 liter/min with the yet unknown concentration
through one inlet. There is one inlet for Tank B. A solution is coming in at the rate of 15 liter/min with the yet
unknown concentration through the inlet. What will be the amount of salt at any given time in the tanks?
(Note: Show the fundamental matrix. Show your results as x(t) for tank A and y(t) for tank B.)

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