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6-028-SaltCompartments-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: concentration comparment salt tank mixing

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Abstract

Resource Image Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.

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Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

Suppose we have two tanks of liquid, Tank 1, holding 100 liters of pure water, and Tank 2, holding 200 liters of pure water - reasonable size fish tanks you might have in your home/office. We dump 100 g of salt (NaCl) into Tank 2, thoroughly dissolve and mix so the salt is uniformly distributed in the tank. Each tank has a capacity of 300 l.

Next we start a pumping action in which we pump 4 l/min of thoroughly mixed saline solution from Tank 1 to Tank 2 and at the same time we pump 3 l/min of thoroughly mixed saline solution from Tank 2 to Tank 1.

Let us assume that a stirrer in each tank keeps the solution thoroughly mixed so that at the very instant saline solution enters a tank its salt is thoroughly mixed in that tank. Let x(t) be the amount of salt in g in Tank 1 at time t in min and y(t) be the amount of salt in g in Tank 2 at time t in min.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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