Quantcast

Atmospheric Dispersion Steady State Concentration

vCalc Reviewed
`C = "Q" /(2pi "u" sigma_y sigma_z ) * e^(-1/2 * "y" ^2/ sigma_y ^2)*[e^(-1/2* ( "z" -( "H" + Delta h ))^2/sigma_ "z" ^2) + e^(-1/2*( "z" +( "H" + Delta h ))^2 / sigma_z ^2)]`
`"Emission Rate"`
`"Horizontal Plume Dispersion Std Dev"`
`"Vertical Plume Dispersion Std Dev"`
`"Average Wind Speed at Stack Height"`
`"Horizontal Distance from Plume Centerline"`
`"Vertical Distance From Ground"`
`"Stack Height"`
`"Plume Rise"`
Tags
Physics

This equation models the general form of the Gaussian Atmospheric Dispersion equation as a function of downwind distance and stability class, meaning the dispersion in crosswind (y) and vertical (z) directions are Gaussian distributions.  The result is the steady-state concentration at a point (x,y,z) expressed in `mu`g/`m^3`.

The effective stack height used is the physical stack's height (H) plus the plume rise (`Delta h`)

Notes

The equation assumes the emission rate is constant, dispersion in downwind (z) direction is negligible, horizontal meteorological conditions (wind speed and direction, temperature, atmospheric stability class and mixing height) are constant, there's no wind sheer un the horizontal or vertical.

We also assume the plume modeling is independent of previous model time, there is no plume deposition at the surface, the pollutants are non-reactive and remain suspended.