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Excel on the same plot. Note: some flow r below; use the conservation of mass to det er what negative eigenvalues imply. What d (what would the math say)? servation equation to develop your differ

Excel on the same plot. Note: some flow r below; use the conservation of mass to det er what negative eigenvalues imply. What d (what would the math say)? servation equation to develop your differ

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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**Problem #3 – Modeling, Mixing Problem** Two tanks are connected by pipes in parallel as shown in Figure 2. Tank 1 starts with 160 lb of salt dissolved in 200 gal of water. Tank 2 starts with 100 gal of pure water. Using the diagram below, solve for the particular solutions of salt concentration in each tank as a function of time. Plot the solutions in Excel on the same plot. Note: some flow rates have been intentionally left out of the diagram below; use the conservation of mass to determine those. As a thought experiment, consider what negative eigenvalues imply. What would it mean if the eigenvalues were positive instead (what would the math say)? i.) Use a conservation equation to develop your differential equation model (you should end up with two ODEs to describe the change in salt in both tanks). ii.) Write your system of ODEs in matrix form. iii.) Set up the eigenvalue problem and then determine the eigenvalues. iv.) Use the eigenvalues to determine the eigenvectors. v.) Write the general solution for the amount of salt in each tank as a function of time. vi.) Use the initial conditions to solve for the particular solutions. vii.) Bonus: plot the solutions in Excel on the same plot. **Figure 2:** Schematic showing two tanks connected by pipes in parallel. Tank 1 has an inlet pumping in pure water. Tank 2 has an outlet through which the salt mixture flows out of. - Tank 1: - Incoming pure water at 6 gal/min - Connections to Tank 2 and outlet - Tank 2: - Outlet for mixed water (salt mixture) The flow rates between the tanks and the mixture outlet are critical to determine the changes in salt concentration in both tanks. Use conservation of mass to determine these rates during modeling.
Transcribed Image Text:**Problem #3 – Modeling, Mixing Problem** Two tanks are connected by pipes in parallel as shown in Figure 2. Tank 1 starts with 160 lb of salt dissolved in 200 gal of water. Tank 2 starts with 100 gal of pure water. Using the diagram below, solve for the particular solutions of salt concentration in each tank as a function of time. Plot the solutions in Excel on the same plot. Note: some flow rates have been intentionally left out of the diagram below; use the conservation of mass to determine those. As a thought experiment, consider what negative eigenvalues imply. What would it mean if the eigenvalues were positive instead (what would the math say)? i.) Use a conservation equation to develop your differential equation model (you should end up with two ODEs to describe the change in salt in both tanks). ii.) Write your system of ODEs in matrix form. iii.) Set up the eigenvalue problem and then determine the eigenvalues. iv.) Use the eigenvalues to determine the eigenvectors. v.) Write the general solution for the amount of salt in each tank as a function of time. vi.) Use the initial conditions to solve for the particular solutions. vii.) Bonus: plot the solutions in Excel on the same plot. **Figure 2:** Schematic showing two tanks connected by pipes in parallel. Tank 1 has an inlet pumping in pure water. Tank 2 has an outlet through which the salt mixture flows out of. - Tank 1: - Incoming pure water at 6 gal/min - Connections to Tank 2 and outlet - Tank 2: - Outlet for mixed water (salt mixture) The flow rates between the tanks and the mixture outlet are critical to determine the changes in salt concentration in both tanks. Use conservation of mass to determine these rates during modeling.
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