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For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank B at a rate of 5L/min, while pure water is discharged to Tank A at a rate of 15L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are 5kg and zero, respectively. • t is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. 1. Setup the system of ODES for the two tanks to determine the amount of pollutant in Tank A and Tank B at any time t. 2. Determine the complementary solution of the corresponding system of ODES. 3. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. 4. What is the final equation of YA(t)? 5. What is the final equation of yB(t)?

For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank B at a rate of 5L/min, while pure water is discharged to Tank A at a rate of 15L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are 5kg and zero, respectively. • t is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. 1. Setup the system of ODES for the two tanks to determine the amount of pollutant in Tank A and Tank B at any time t. 2. Determine the complementary solution of the corresponding system of ODES. 3. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. 4. What is the final equation of YA(t)? 5. What is the final equation of yB(t)?

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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Please help me answer the first three questions. Thank you!

Pure Water 0.5 kg/L Pollutant 15 L/min 5 L/min 1000 L 15 L/min 1000 L with 5 kg pollutant Pure Water Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank B at a rate of 5L/min, while pure water is discharged to Tank A at a rate of 15L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are 5kg and zero, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. 1. Setup the system of ODES for the two tanks to determine the amount of pollutant in Tank A and Tank B at any time t. 2. Determine the complementary solution of the corresponding system of ODES. 3. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. 4. What is the final equation of YA(t)? 5. What is the final equation of yB(t)?
Transcribed Image Text:Pure Water 0.5 kg/L Pollutant 15 L/min 5 L/min 1000 L 15 L/min 1000 L with 5 kg pollutant Pure Water Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank B at a rate of 5L/min, while pure water is discharged to Tank A at a rate of 15L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are 5kg and zero, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. 1. Setup the system of ODES for the two tanks to determine the amount of pollutant in Tank A and Tank B at any time t. 2. Determine the complementary solution of the corresponding system of ODES. 3. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. 4. What is the final equation of YA(t)? 5. What is the final equation of yB(t)?
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