We have a stored quantity of something, like water in a temporary pond, which is percolating into the ground. As the pressure driving it decreases, the water draws out - quickly at first and then more slowly.

This model (Figure III-1) is a version of TANK (Figure I-2) but with only one pathway, an outflow. When the run starts, the storage drains rapidly and then more slowly because a constant percent (K) of what is remaining (Q) flows out in each unit of time.

The resulting graph of the change in Q (Figure III-1b) is a declining exponential.

Examples of Draining Tank Models

An example is water diffusing through sand. As a wave comes up on the beach, the water drains into the sand quickly. As the pressure of the wave water decreases, its flow into the sand slows. Decomposition of a pile of leaves by microbes fits this model.

Another example is the decay of elements like uranium. It is measured in half7lifes. Uranium 238 has a half-life of 4 billion years. That means that in 2 billion years half of a sample has decayed to lead. In the next 2 billion years only half of what's left will decay.

Here is an economic example. You are given a bank account from ­which you spend a certain percent every month. Your account would go down like this graph.

Some population of the number of individuals will have a survival curve that fits this model. The survival curve is the fraction of those born at the same time, which are still living at a later time.

In pollution studies a rough but widely used method of measuring organic matter in waters is the measurement of BOD (biochemical oxygen demand). When water is put into a bottle and then kept in the dark, decomposition (respiration occurs in proportion to the amount of organic matter available. The oxygen used up after five days is used as a comparative measure of the organic matter originally present. The change of oxygen in the bottle follows this graph (Figure III-1).

"What if" Experimental Problems

1. If you started with a larger pile of leaves in the forest, with the same rate of decomposition, would the pile be gone sooner, at the same time, or later? Change Q to 160 and run.
   


2. Double the rate of your spending of your bank account (Change K to 0.02). How long does your money last?
   

COMPUTER MINIMODELS AND SIMULATION EXERCISES FOR SCIENCE AND SOCIAL STUDIES

Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007