Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres 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-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting pipe, the well-stirred solution in Tank X drains out at a rate of 8 litres/min,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(a) Draw a diagram that depicts the flow process described above. Let QX(t) and QY(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for QX and QY that model the flow process. Justify if the system of differential equation is homogeneous or non-hompgeneous

1.
Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20
litres 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-stirred
solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different
connecting 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 remainder
leaves the system.
Transcribed Image Text:1. Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres 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-stirred solution flows from Tank Y to Tank X at a rate of 8 litres/ min. Through a different connecting 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 remainder leaves the system.
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