Mixing in Two Tanks

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Tank A contains 50 liters of brine in which 25 grams of salt are dissolved. Tank B contains 50 liters of brine in which 0 grams of salt are dissolved. Fresh water is pumped into tank A at a rate of 4 liters/minute; the well-mixed solution is pumped from tank A into tank B at 4 liters/minute. The well-mixed solution from tank B is pumped out at 4 liters/minute. This Demonstration uses colors and animation to visualize the solution to this problem.

Contributed by: Stephen Wilkerson  (March 2011)
(United States Military Academy West Point)
Open content licensed under CC BY-NC-SA



This problem was taken from the MA205 course examples at the United States Military Academy, West Point. It involves a model of a multi-tank mixing problem using a system of first-order differential equations. Students are asked to solve the equations using a variety of methods. This Demonstration provides a visualization of the mixing example given as a reading assignment to help prepare the students. This problem would be a good example for any course that includes coupled first-order differential equations. It lets an instructor simulate a visual experiment without the mess of setting up a lab in the classroom. Students can solve these equations using a variety of methods including numerical, Laplace transforms, eigenvalues and eigenvectors, and elimination.


D. Zill, A First Course in Differential Equations with Modeling Applications, 9th ed., Pacific Grove, CA: Thomson Brooks/Cole, 2008.

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