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Gaussian Plume Dispersion Equations Formulas

This below equation assumes that Dispersion will continue vertically even below the ground level.

The truth is that vertical spreading terminates at ground level.

This method is equivalent to assuming that a mirror iimage plume exists below the ground.

The added new concentration due to the image plume uses z+H instead of z-H.

Gaussian Max Ground Level Emission Concentration Formulas

The ground-level concentrations directly downwind are of interest, since pollution concentration will be highest along that axis.

Using the below equation , the effect of variations in the key parameters (atmospheric stability, wind speed, ambient temperature, stack height, gas exit velocity, and gas exit temperature) on the ground concentrations are calculated.

where,

C is maximum ground level concentration of emission at point(x,y,z) in μg/m³

Q is emission rate μg/s.

σ_y is horizontal dispersion of emission in m.

σ_z is vertical dispersion of emission in m.

π = 3.141592653589793238

U is average wind speed at stack height in m/s.

H is effective stack height in m.

H = ∆h + h

∆h is plume rise in m.

h is physical stack height in m.

σ_z is H ÷ √2 for neutral atmospheric conditions.