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Gaussian Equation:

The highest
concentration is the center of the plume at ground level
(y=0, z=0, h=0), where the equation is:

Step 1. Enter the input
variables:

Q =
emission rate =grams/sec

pi =3.14159...

u =
average wind speed =meters/sec

x =
downwind distance =meters

Atmospheric Stability (A-F)
=

Step 2. Record sigma values (note: ^ means "to the power of"):

sigma y = [*^] =

sigma z = [*^]- =

Step 3.
Results

Conc. = / [ 2 * 3.14159
***] =
micrograms /
m^{3}

Sigma values

Sigma values are fundamental to all gaussian based air
dispersion models. They can be determined very roughly by reading off
a graph, but are more accurately determined by the following
equations:

The value of x is always the distance downwind
from the source. The values of a, c, d, and f are determined
experimentally and amount to curve-fitting. These numbers are found
in tables, and there are various sets of tables. It can be rather
tedious to find the values of a,c,d,and f that correspond to the
atmospheric stability being studied, so we can be thankful that
various computer programs determine these values for us. However, if
you want to see the tables used in this particular calculator and use
a calculator to solve the above function, try the
power
function calculator.

One final comment: it's not difficult to see various
discussions of gaussian air dispersion models on the internet. The
approach I've presented here emphasizes the conceptual basics, and a
brief search will show that there are various manipulations of this
basic guassian equation. One of the most frequently used gaussian
based models is aptly named "screen3", which we will discuss a little
later on.