10182

# Mixing in Two Connected Tanks

Pipes carrying brine at different rates and concentrations connect two tanks.
The diagram (see Figure 3.2.9 in [1]) shows the initial concentrations of salt, the volumes of brine, the flow rates and the concentrations of brine flowing in, and the flow rates between the tanks and going out.
Let and be the amount of salt (in ounces) in tanks 1 and 2. The equations for the time rates of change of and are
,
.
The constant coefficients , , , , , are related to the various rates of flow as follows:
This Demonstration shows the resulting salt solution in each tank by a change in color and in the graph. The system tends to steady state over time. For example, set the input brine to zero for both tanks and watch as the solution in both goes to zero. The steady state can be obtained deductively for some solutions.

### DETAILS

This example comes from [1], Section 3.2, Fluid Flow in Tanks, following problem 30.
Reference
[1] J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, New York: John Wiley and Sons, 2010.

### PERMANENT CITATION

Contributed by: Stephen Wilkerson
(United States Military Academy West Point, Department of Mathematics)
 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.