Mixing in Two Tanks

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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.


    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+