Averaging for Wind Speed in a Given Direction in the Concentration Equation for Pollutants

Abstract

In the equation for the concentration of pollutants from a steady continuous point source, in a stationaryturbulent flow, the factor 1/u enters (u is the mean wind for a given stationary situation). If we are interestedin the concentration along a given wind direction and u denotes the wind speed in that direction and if weseek the average concentration for a class of flow situations (e.g., for the class of statically stable flows),each member of the class representing an individual stationary situation, then the averaging to be appliedis to 1/u and not to u. On the assumption (verified by some examples) that the distribution of u isa "humped" gamma distribution (standard deviation σ less than the average u of u for the class as a whole),we show that the average of 1/u equals 1/(u[1-(σ/u)2]}. Thus the average of 1/u is greater than 1/uand the resulting concentration estimate is larger than the one that would be obtained by the incorrect useof 1/u.