Mixing Salt in Water in One Tank

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This example comes from [1], Section 2.2, Modeling with First Order Equations.

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The equation is

,

where is time in minutes, is the amount of salt in the tank at time , is the rate of flow in and out of tank in gallons per minute. At time the tank contains pounds of salt in a tank containing 100 gallons of water. Assume that the tank is well stirred. In this example the mixture flowing into the tank contains 1/4 pound of salt per gallon, so one would expect that the tank will eventually contain 25 pounds of salt.

Dragging the locator on the right changes the initial amount of salt found in the tank.

More than 1/4 pound of salt per gallon is colored dark orange or brown while less than 1/4 pound per gallon is colored dark green.

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Contributed by: Stephen Wilkerson (December 2010)
(United States Military Academy West Point, Department of Mathematics)
Open content licensed under CC BY-NC-SA


Details

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.


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