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Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and 40 gallons of pure water respectively. A brine with salt concentartion of 1lb/gal flows into the first tank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank with the rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with the rate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate 3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys- tem of differential equations describing the amount of salt in each tank and put it into the matrix form.

Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and 40 gallons of pure water respectively. A brine with salt concentartion of 1lb/gal flows into the first tank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank with the rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with the rate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate 3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys- tem of differential equations describing the amount of salt in each tank and put it into the matrix form.

Advanced Engineering Mathematics
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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Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and 40 gallons of pure water respectively. A brine with salt concentartion of 11b/gal flows into the first tank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank with the rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with the rate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate 3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys- tem of differential equations describing the amount of salt in each tank and put it into the matrix form. mixture 11b/gal flow 5 gal/min 10 gal 8 gal/min J 20 gal 3 gal/min 8 gal/min 40 gal 5 gal/min
Transcribed Image Text:Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and 40 gallons of pure water respectively. A brine with salt concentartion of 11b/gal flows into the first tank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank with the rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with the rate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate 3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys- tem of differential equations describing the amount of salt in each tank and put it into the matrix form. mixture 11b/gal flow 5 gal/min 10 gal 8 gal/min J 20 gal 3 gal/min 8 gal/min 40 gal 5 gal/min
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