In this article we will discuss about the diffusion theories in relation to air pollution control.

The dilution of pollutants directly depends on the atmosphere turbulence and diffusion. Therefore the dilution varies with the weather conditions. As the rates of atmosphere dilution determines the levels of pollution in a given location, methods for estimating the degree of atmosphere diffusion are of a paramount importance.

There are various formulae based on various assumptions to determine ground level concentration from a known source emission for various stability classes.

**Following Gaussion diffusion equation is the basic equation from which other equations are derived: **

Q = emission rate (gm/sec)

= cross-wind and vertical plume standard direction (m)

u = mean wind speed (m/sec.)

h_{e} = effective height of stack (m)

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C = concentration ground level (gm/m^{3})

For ground level concentrations (Z= 0) and along the centre line of plume axis (y = 0), the above equation becomes,

With stability class, the values for σ_{y} and σ_{z }varies. Table 7.1 gives the stability characteristics of the atmosphere.

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The values of σ_{v} and σ_{z}, varies with distance from emission point. σ_{y} and σ_{z} values are taken for the particular stability class and distance. The ground level concentrations at various distances for the prevailing stability class are calculated and shown graphically.

The effective stack height is the actual stack height plus rise.

**The calculation of the plume rise is done on the basis of momentum, rise and buoyancy rise as follows: **

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**Momentum rise:**

Where x is greater than 2.∆H_{m}max

h = Stack height above ground level in m

∆h_{m} = Momentum rise in m

∆h_{b} = Buoyancy rise in m

u = Wind speed at location in m/sec.

V_{3} = Stack exit velocity in m/sec.

X = Down-wind distance from stack in m

Q_{h} = Emission rate of pollutants in gms/sec.

Q_{vl }= Emission rate of stack gas at temp. T_{1} gms/sec.

T_{a} = Absolute ambient temp, in °K

T_{1}= Absolute stack gas temp, in °K

T_{3} = Absolute temp, of stack gases in °K

g = Acceleration due to gravity

d_{b}/d_{3} = Potential temp, gradient of ambient air in °C/m.

This equation was developed by Bonasquest and is valid for stable atmospheric conditions.

**Holland has developed plume rise equation for neutral condition, as follows: **

where Δh = plume rise in m

p = Atmospheric pressure in mm of Hg.