Mean wind speed

7 FUNCTIONAL FORMS OF MEAN WIND SPEED AND EDDY DIFFUSIVITIES 

While the Gaussian equations have been widely used for atmospheric diffusion calculations, the lack of ability to include changes in wind speed with height and nonlinear chemical reactions limits the situations in which they may be used. The atmospheric diffusion equation provides a more general approach to atmospheric diffusion calculations than the Gaussian models, since the Gaussian models have been shown to be special cases of that equation when the wind speed is uniform and the eddy diffusivities are constant. The atmospheric diffusion equation in the absence of chemical reaction is 

The mean wind speed, usually taken as that coinciding with the x direction, is often represented as a power-law function of height by (16.78), 

The expressions available for are based on Monin-Obukhov similarity theory coupled with observational or computationally generated data. It is best to organize the expressions according to the type of stability. 

Since we generally need expressions for K that extend vertically beyond the surface layer, we now consider some available correlations for the entire Ekman layer. 

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Aerodynamic Downwash Should the stack exit velocity be too low as compared with the speed of the crosswind, some of the effluent can be pulled downward by the low pressure on the lee side of the stack. This phenomenon, known as stack-tip downwash, can be minimized by keeping the exit velocity greater than the mean wind speed (i.e., typically twice the mean wind speed). Another way to minimize stack-tip downwash is to fit the top of the stack with a flat disc that extends for at least one stack diameter outward from the stack. 

Note Generally, the ratio of rated to mean wind speed may be quite high due to long lean periods, when the maehine may slay idle, redueing the value of the mean speed. 

In this case a-y is 419 m. The peak concentration can be found from the measurements, or from the Gaussian distribution fitted to the data and the peak concentration obtained from the fitted distribution. Provided that the emission rate Q, the height of release H, and the mean wind speed u are known, the standard deviation of the vertical distribution of the pollutant can be approximated from either the peak concentration (actual or fitted) or the cross wind integrated (CWI) concentration from one of the following equations ... 

In its most common form, a trajectory model moves a vertical column, with a square cross section intersecting the ground, at the mean wind speed, with pollutants added to the bottom of the column as they are generated by each location over which the column passes. Treatment of vertical dispersion varies among models, from those which assume immediate vertical mixing throughout the column to those which assume vertical dispersion using a vertical coefficient with a suitable profile (15). 

Mean wind speed and direction The air flow is assumed to be horizontal, but the flow may be tilted (to yield a vertical component) due to local topographic effects. The mean wind speed determines the convection of the stack emissions. 

These meteorological parameters, with the possible exception of the mean wind speed and direction, are not generally available for inclusion in calculations. Even wind speed measurements, which are usually taken at 20 ft above grade, must be corrected to the release point elevation. The correction applied to the wind speed depends on the turbulence of the air. The wind speed is the key determinant of the convection of pollutant in a plume. 

We shall now provide a second example to illustrate step-by-step calculations. In this example a flare stack is estimated to be 80% efficient in combusting HjS off-gas. The total off-gas through the stack is 400,000 kg/hr, of which 7.0 weight percent is H2S. The physieal stack height is 250 m, the stack diameter is 5.5 m, and the stack emission velocity is 18 m/s. The stack emission temperature is 15°C. The meteorological conditions may be described as a bright sunny day with a mean wind speed of 3 m/s. 

Wind has a highly turbulent and gusting character. In addition, a time-mean speed varies with the height from the ground and the roughness of the terrain over which the wind passes. The time-mean wind speed profile can be determined using the following expression ... 

To evaluate the wind speed at height H it is necessary to know the value of for the required location. This may be obtained either from a local weather station or from wind contour maps of the country. Normally, represents the hourly mean wind speed that is exceeded 50% of the time at a particular site. 

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. 

U = mean wind speed affecting plume (m), z = standard deviation of plume concentration in the vertical at distance X (m), y = standard deviation of plume concentration in the horizontal at distance X (m),... 

Basing models on zonal mean wind speed and sea surface temperature is averaging over regions where very different regimes of interaction of wind speed, SST and volatilisation rate prevail. In a long-term mean this leads to an underestimation of the volatilisation rate and its variabilty. 

A solution of Eq. (9.36) has been obtained by Huang (1979) in the case when the mean wind speed and vertical eddy diffusivity can be represented by the power-law expressions ... 

The Gaussian plume model estimates the average pheromone flux by multiplying the measured odor concentration by mean wind speed, using the following formula (Elkinton etal, 1984). Everything is the same as in the Sutton model, except that ay and az, respectively, replace the terms Cy and Cz of the Sutton model. Dispersion coefficients are determined for each experiment separately. 

For compounds with Kii/Vl larger than about 10 2 the overall air-water transfer velocity is approximately equal to the water-phase exchange velocity viw The latter is related to wind speed uw by a nonlinear relation (Table 20.2, Eq. 20-16). The annual mean of viw calculated from Eq. 20-16 with the annual mean wind speed ul0 would underestimate the real mean air-water exchange velocity. Thus, we need information not only on the average wind speed, but also on the wind-speed probability distribution. 

Somebody wants to calculate monthly means of air-water exchange velocities from monthly mean wind speed data. What is the problem ... 

Mean wind speed Air-water transfer velocity for 10 5 m s 1... 

Drift Budget. Four tests were conducted in atmospheric conditions which ranged from slightly stable through neutral to moderately unstable but with very similar mean wind speeds at 46 m above ground. The results of Crabbe et al. (7) for the airborne fraction of the applied spray are shown in Table II. At 400 m downwind of the swath 31 % of the material is still airborne while under neutral and unstable conditions the drifting fraction decreased to 12% and 9%, respectively. This trend is supported by measurements at 1200 m where under neutral atmospheric conditions 10% of the spray is still drifting while in the unstable case, no airborne droplets were detectable at this distance. 

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