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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.

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.

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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0.5 kg/L Pollutant Pure Water 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 100OL volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/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 zero and 5kg, respectively. • Itis 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.
Transcribed Image Text:0.5 kg/L Pollutant Pure Water 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 100OL volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/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 zero and 5kg, respectively. • Itis 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.
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