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CENE 330 Air Quality Engineering

Homework #4 – AP Dispersion Models

Assigned: November 15, 2016

Due: November 29, 2015

Problem Description

Objective: The objective of this homework assignment is to

1) Evaluate the differences occurring between two different methods for determining the dispersion coefficients, σy and σz, when using the same Gaussian dispersion modeling

equation.

2) Create a basic modeling tool in a spreadsheet for conducting quick evaluations of an elevated air pollutant point source.

Approach:

1) This assignment is to be completed in groups of 2 persons.

2) Complete Objective 1 as follows. Use the AJ Design Atmospheric Dispersion Calculator

for the contaminant concentration at ground level along a plume centerline from an

elevated source. Enter dispersion coefficients, σy and σz, from Method 1 and Method 2,

(see Resources below) as well as the following stack data; pollutant (SO2) emission rate =

150 g/s, wind speed at effective stack height = 3.3 m/s, effective stack height = 150

meters. Create 3 separate plots (using Excel and the data you generate) to compare

these two methods of determining the dispersion coefficients, σy and σz, under the

stability conditions A, D and F, and for downwind distances from 10 meters to 20 km.

Base your plots on at least 12 separate distances (10m and 20 km are required

distances).

3) Complete Objective 2 as follows. Based on the approach presented in Kumar, K (1994)

“Get a fix on plant pollutants,” in Chemical Engineering, vol. 101, no. 11, pp 141, for an

elevated source, design and create a spreadsheet model that estimates ground-level

concentrations between 0 and 800 meters downwind from a source along the

centerline. Include the ability to input stability conditions A, D or F. Include a single

chart that displays the downwind concentrations (x-axis = distance, y-axis =

concentration) for different wind speeds from 0.5 m/s to 15 m/s (each wind speed will

result in a line within the final plot). Include enough points in each line plotted to create

a relatively smooth line plot.

4) To complete this overall assignment, prepare a short report with the following contents:

a) Include the 3 plots created for Objective 1. Describe and explain any differences

that you find between the two methods for estimating the dispersion coefficients.

b) Include the plot created for Objective 2. Describe and explain what you observe

about the influence of wind speed and stability condition.

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Resources: The following resources must be used when working on this problem.

1) The AJ Design “Atmospheric Dispersion Calculator” located in BbL as shown in class.

2) Dispersion Coefficients Estimation Method 1. The following information for estimating

the dispersion coefficients is based on Martin, D.O. (1976) Comment on “The change of

concentration standard deviation with distance,” JAPCA, vol. 26, no. 2, pp145-147.

σy = horizontal dispersion coefficient

σz = vertical dispersion coefficient

Both of these dispersion coefficients are a function of stability and distance.

σy can be calculated (estimated) using the following general equation.

σ� = �� �

σz can be calculated (estimated) using the following general equation.

σ� = �� � +

The constants a, b, c, d and f are dependent on stability and distance and are obtained

using the following table.

x < 1 km x > 1 km

Stability a b c d f c d f

A 213 0.894 440.8 1.941 9.27 459.7 2.094 -9.6

B 156 0.894 106.6 1.149 3.3 108.2 1.098 2.0

C 104 0.894 61.0 0.911 0 61.0 0.911 0

D 68 0.894 33.2 0.725 -1.7 44.5 0.516 -13.0

E 50.5 0.894 22.8 0.678 -1.3 55.4 0.305 -34.0

F 34 0.894 14.35 0.740 -0.35 62.6 0.180 -48.0

3) Dispersion Coefficients Estimation approach used for Method 2 is given in Kumar, K

(1994) “Get a fix on plant pollutants,” Chemical Engineering, vol. 101, no. 11, pp 141,

located in BbL as shown in class.