1-042-S-Kool-Aid

By Kristin Burney1, Lydia Kennedy1, Audrey Malagon1

1. Virginia Wesleyan College, Norfolk VA USA

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Abstract

Single-compartment mixing is an important foundational component of any study of ordinary differential equations. Typically, problems utilize salt as the solute. In this modeling scenario, use of colored drink powder as the solute enables students to observe a color change as the mixing progresses. Students run two experiments that involve a concentrated solution of drink powder flowing from an upper tank to a lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks and record initial conditions. In the first experiment, the spout on the lower tank remains closed; in the second, the solution flows from both tanks at the same flow rate. Prior to experimentation, students are asked to predict the outcomes and sketch results. Following experimentation, students develop mathematical models and use them to determine the amount of drink powder in the lower tank at the end of each experiment. Specifically, first-order separable and linear differential equations are employed. Additional components of the lab invite students to consider a situation in which tank outflow rates differ (i.e., changing tank volume over time) and, further, a scenario in which pollution is entering and leaving a lake via streams.

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Researchers should cite this work as follows:

  • Kristin Burney; Lydia Kennedy; Audrey Malagon (2017), "1-042-S-Kool-Aid," https://www.simiode.org/resources/3526.

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