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# SIMIODE

## OER Materials

Modeling Scenario

## 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

## Abstract

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

## Citation

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## 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.

## Authors

Author(s): Brian Winkel

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