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Consortium for Mathematics and its Applications

Product ID: ILAP
Supplementary Print
Undergraduate
High School

Chloroform Alert! (ILAP)

Author: John R. Liukonnen, Laura J. Steinberg


AAA Chemical Inc. operates two chemical plants in the town of Bayou St. Edwards, home of Dixieland State University. New pollution monitoring equipment has shown elevated concentrations of chloroform in the air over the university. These concentrations are considered unhealthy, and the student Engineering Society has formed a study group to review the problem. They have come up with a number of possible ways to reduce the pollution, including relocating the plants, making the smokestacks taller, and adding air pollution control equipment to the plants. They want to analyze the costs and compute the reduction in chloroform concentration that is expected from each possible solution. You are asked to help them with the project by completing Parts 1, 2, 3, and 4 below.

In Part 1, you learn how to model chloroform concentrations in the atmosphere in the presence of diffusion and turbulence

In Part 2, you add the effect of wind to the model

Part 3 shows how the model can be simplified in the case of steady-state conditions (no change in chloroform emissions over time), and how the chloroform emissions from the two chemical production plants can be added together to calculate the combined effect of the two plants on air quality.

In Part 4, you apply the simplified model to Dixieland University. You are asked to calculate concentrations of chloroform in the air over the university and to choose between various engineering remedies.

Physical Concepts Examined:
1. Advection
2. Diffusion
3. Steady-state modeling
4. Simulation of contaminant transport

Table of Contents:

SETTING THE SCENE

PART 1: DIFFUSION AND TURBULENCE VIA DISCRETE APPROXIMATION

PART 2: ADVECTION VIA DISCRETE APPROXIMATION

PART 3: SUPERPOSITION AND STEADY STATE

PART 4: DATA

SAMPLE SOLUTIONS

NOTES FOR THE INSTRUCTOR

ABOUT THE AUTHORS

©2002 by COMAP, Inc.
The UMAP Journal 23.2
20 pages

Mathematics Topics:

Calculus , Probability & Statistics

Application Areas:

Engineering & Construction , Environment & Sustainability , Environmental Engineering

Prerequisites:

1. Computing means and variances of random variables
2. Understanding partial derivatives
3. Finding Taylor series approximations
3. Understanding the Central Limit Theorem

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