Atmospheric Dispersion Equations for Continuous Sources

There are many dispersion equations available, most of them semiempirical. It is not tlie intent of this book to develop each in detail but ratlier to look at tlie one tliat has found tlie greatest applicability today. (In the authors opinion, tlie best atmospheric dispersion workbook published to dale is that by Turner (8)) 

The concenlration c of gas or aerosols at (x, y, z) from a continuous source with an effective emission height, H is given by  

The assumptions made in tlie development of Eq. 12.6.1 are (1) tlie plume spretid lias a Gaussian distribution in both tlie horizontal and vertical planes witli standard deviations of plume concentration distribution in the horizontal and vertical of Oy and respectively (2) tlie emission rate of pollutants Q is uniform (3) total reflection of tlie plume takes place at tlie eartli s surface and (4) tlie plume moves downwind with mean wind speed u. Altliough any consistent set of units may be used, tlie cgs system is preferred. 

Equation is valid where diffusion in tlie direction of tlie plume travel can be neglected (i.e., no diffusion in the x direction). This is a valid assumption if tlie release is continuous or if tlie duration of release is equal to or greater tlian the travel time x / u from flic source to tlie location of interest. 

In tlie case of a ground level source with no effective plume rise (H = 0), tlien 

1 (Note tliat this is the coordinate system used by most engineers.) The origin is at ground level at or beneath the point of emission, with the x a.xis extending liorizonially in the direction of the mean wind. Tlie y axis is in tlie horizontal plane perpendicular to tlie x axis, and tlie z axis extends vertically. The plume travels along or parallel to the x axis (in tlie mean wind direction). 

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A rather significant amount of data and information is available for sources that emit continuously to the atmosphere. See Chapter 48 for more details. Unfortunately, little is available on instantaneous or puff sources. Other than computer models that are not suitable for classroom and/or illustrative example calculations, only Turner s Workbook of Atmospheric Dispersion Estimates, USEPA Publication No. AP-26, Research Triangle Park, NC, 1970 provides an equation that may be used for estimation purposes. Cases of instantaneous releases, as from an explosion, or shortterm releases on the order of seconds, are also and often of practical concern. 

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