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A at rate 5 litres per minute. ire water pumped into it at a rate 5 litres from it at rate 15 litres per minute. o kg of salt is dissolved imto tank A. and

A at rate 5 litres per minute. ire water pumped into it at a rate 5 litres from it at rate 15 litres per minute. o kg of salt is dissolved imto tank A. and

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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4. Consider two tanks A and B, each holding 200 litres of water. A pipe pumps brine from tank A to tank B at a rate of 20 litres per minute. At the same time another pipe pumps brine from tank B to tank A at rate 5 litres per minute. In addition, tank A has pure water pumped into it at a rate 5 litres per minute and tank B has brine pumped out from it at rate 15 litres per minute. At time t = 0, ro kg and y, kg of salt is dissolved into tank A, and tank B, respectively. (a) Write down the system of differential equations satisfied by r(t) and y(t), the quan- tity of salt in tank A and B, respectively. (Hint: Draw a picture would help !) (b) Find the eigenvalues and eigenvectors of the resulting matrix from. (c) Draw the phase portrait in the (x, y) coordinate for this system. (d) Describe the amount of salt in each tank when the time approaches infinity.
Transcribed Image Text:4. Consider two tanks A and B, each holding 200 litres of water. A pipe pumps brine from tank A to tank B at a rate of 20 litres per minute. At the same time another pipe pumps brine from tank B to tank A at rate 5 litres per minute. In addition, tank A has pure water pumped into it at a rate 5 litres per minute and tank B has brine pumped out from it at rate 15 litres per minute. At time t = 0, ro kg and y, kg of salt is dissolved into tank A, and tank B, respectively. (a) Write down the system of differential equations satisfied by r(t) and y(t), the quan- tity of salt in tank A and B, respectively. (Hint: Draw a picture would help !) (b) Find the eigenvalues and eigenvectors of the resulting matrix from. (c) Draw the phase portrait in the (x, y) coordinate for this system. (d) Describe the amount of salt in each tank when the time approaches infinity.
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