Atmospheric Dispersion Equation for Instantaneous Sources

The previous section considered only sources that emit continuously. A ratlier significant amount of data and information is presented diere. Unfortunately, little is available on instantaneous or puff sources. Turner s Workbook (8) provides an equation tliat may be used for estimation purposes. This approach is presented below. 

Only sources emitting continuously or for periods equal to or greater tlian tlie travel times from tlie source to the point of interest were treated earlier. Cases of instantaneous release, as from an explosion, or short-tenn releases on tlie order of seconds, are also and often of practical concern. To detennine concentrations at any position downwind, one must consider tlie time interval after tlie time of release and diffusion in the downwind direction as well as lateral and vertical diffusion. Of considerable importance, but very difficult, is tlie detennination of the patli or trajectory of tlie puff. Tliis is most important if concentrations are to be determined at specific points. Detennining tlie trajectory is of less importance if knowledge of tlie magnitude of tlie concentrations for particular downwind distances or travel times is required but tlie exact points at which these concentrations occur need not be known. An equation that may be used for estimates of concentration downwind from an instantaneous release from height H is 

Others have suggested values for a Oy and Oz for qiuisi-instantaneous sources. These are given in Table 12.7.1. Tlie problem remains to make best estimates of a. Much less is known of diffusion in the downwind direction than is known of lateral and vertical dispersion. In general, one should expect the value to be about the same as Oy. 

Initial dimensions of the puff (e.g., from an explosion) may be approximated by finding a virtual distance similar to that for area sources to give the appropriate initial standard deviation for each direction. Then ay will be determined as a function of v +. y, a. as a function of v + Xz and a as a function of x + Xz. 

TABLE 12.7.1 Estimation of Dispersion Parameters for Quasi ln.stantaneous Sources 

xperience in designing stacks lias accumulated over tlie years, several rules of thumb luu e evolved 

Stack heights should be at least 2.5 times the height of any surrounding buildings or obstacles so that significant turbulence is not introduced by these factors. 

The a s in Eq. (12.7.1) refer to dispersion statistics following the motion of the expanding puff. Tire o.x is the standard deviation of the concentration distribution in tlie puff in the downwind direction, and t is tlic time after release. Note that tlierc is no dilution in tlie downwind direction by wind speed. Tlie speed of the wind mainly serves to give the downwind position of the center of the puff, as shown by c.xaniination of the exponential involving a. Wind speed may influence the dispersion indirectly because the dispersion parameters and az may be functions of wind speed. The OyS and Oz s 

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Equation (2.2) can be considered as the fundamental governing equation for the concentration of an inert constituent in a turbulent flow. Because the flow in the atmosphere is turbulent, the velocity vector u is a random function of location and time. Consequently, the concentration c is also a random fimction of location and time. Thus, the dispersion of a pollutant (or tracer) in the atmosphere essentiaUy involves the propagation of the species molecules through a random medium. Even if the strength and spatial distribution of the source 5 are assumed to be known precisely, the concentration of tracer resulting from that source is a random quantity. The instantaneous, random concentration, c(x, y, z, t), of an inert tracer in a turbulent fluid with random velocity field u( c, y, z, t) resulting from a source distribution S x, y, z, t) is described by Eq. (2.2). 

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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