Area-averaged concentration

Surface microlayer samples have shown sulphur-gas anomaly patterns that are more closely related to known mineralisation than sulphur-gas patterns from deeper soil samples (Lovell, 1979). At Johnson Camp, Arizona, mineralisation is best expressed by sulphur compounds from the surface microlayer, while sulphur compounds from 0-5 cm reflect the same mineralisation to a lesser extent, and sulphur compounds from 30-40 cm show the least expression of the mineralisation. A comparison of concentrations of COS, CS2, and SO2 degassed from soils collected at depths of 0.5-2 cm and 30-40 cm at the same sites near Casa Grande, Arizona, showed almost identical patterns of sulphur-gas concentrations over a 150 km (58 square miles) area. Average concentrations of COS, CS2 and SO2 were slightly higher in the shallow samples than in the deeper samples (Hinkle, unpublished data, 1981). These data indicate that, at least in arid areas, surficial soil and microlayer samples are superior to deeper augered samples. 

The poblem stated above is sufficiently complex that a closed-form analytical solution in the time domain has not been found. For most purposes, the details of the radial distribution of solute are unimportant, and a description of the longitudinal dispersion of solute in terms of a local mean concentration (that is, radially averaged) will suffice. The most mathematically convenient mean concentration is an area-averaged concentration, defined as... 

The equations derived from radial averaging still contain the local concentration as a variable. To proceed further, approximations are developed to relate the local concentration to the area-averaged concentration. The approach used in earlier models... 

To complete our analysis of equation 1.91, we need to know how the area-averaged concentration, is related to the volume-averaged concentration, (c y) . When... 

In most electrophoretic experiments, the quantity of practical interest is the cross-sectional area-averaged concentration distribution of sample ions. This quantity is, for example, proportional to the... 

Cij and Di represent the area-averaged concentration, the intersticial velocity and the dispersion coefficient, in channel i. It woiild be interesting to derive a similar equation for bed scale averaged variables. Unfortunately, it is impossible to derive such equation in an exact manner because diffusion and percolation processes are ruled by fundamentally different elementary mechanisms, (see e.g. Broadbent et al., 1957). Actually, the stochastic model defined by Eq.5 > describes the liquid velocity distribution and could also be used to characterize nximerically the distribution of residence times i.e., the dispersion process. Achwal et al. (1979) drew attention to a procedure using a Markov chain model which led to similar results for the velocity distribution. This model remained essentially numerical and rather cumbersome. Even if Eq.5 has a simple analytical form, its mamerical application to estimate the dispersion process is also too complex for practical purposes. 

Brighton P. W. M. 1985. Area Averaged Concentrations, Height Scales, and Mass Balances, Journal of Hazardous Materials, vol. 11, pp. 189-208. 

Suppose we define the rate of radial growth of the crystalline disks as r. Then disks originating from all nuclei within a distance rt of an arbitrary point, say, point X in Fig. 4.6a, will reach that point in an elapsed time t. If the average concentration of nuclei in the plane is N (per unit area), then the average number of fronts F which converge on x in tliis time interval is... 

The quantity soibed ATf is simply the volume of polymer affected times the average concentration. The volume affected is the package area... 

Residence time distiabution (RTD) In the case of elutriation of tracer from a vessel that contained an initial average concentration the area under a plot of E t) = between the ordinates at ti and to is the fraction of the... 

Larsen (18-21) has developed averaging time models for use in analysis and interpretation of air quality data. For urban areas where concentrations for a given averaging time tend to be lognormally distributed, that is, where a plot of the log of concentration versus the cumulative frequency of occurrence on a normal frequency distribution scale is nearly linear,... 

The behavior of these pollution roses is intuitively plausible, because considerable hydrocarbon emissions come from motor vehicles which are operated in both winter and summer and travel throughout the urban area. On the other hand, sulfur dioxide is released largely from the burning of coal and fuel oil. Space heating emissions are high in winter and low in summer. The SO2 emissions in summer are probably due to only a few point sources, such as power plants, and result in low average concentrations from each direction as well as large directional variability. 

About 15 gallons of TCE can impact an area 1,000 meters in length, 100 meters in width, and 20 meters in depth with an average concentration of 100 ppb, or roughly 528 million gallons... 

In the case of tracer from a vessel that contained an initial average concentration C°, the area under a plot of E(t) = Cgff[ygj,/C° between the ordinates at tj and tj is the fraction of the molecules that have residence times in this range. In the case of step constant input of concentration Cf to a vessel with zero initial concentration, the ratio F(t) = Cgff ygj,/Cf at tj is the fraction of molecules with residence time less than tj. 

A Similar aphical presentation of the spatial distribution of a tracer g is or a real contaminant and thereby to some extent the airflow in the studied area is based on the use of computed tomography and optical remote sens-jt]g I2.M beams are sent out horizontally and reflected back to an IR analytical instrument, analyzing the average concentration of the contaminant along the IR beam. By combining data from several measured tines it is possible ro present data in a similar way to Fig. 12.8. Those methods presuppose access ro an expensive and complicated sampling/data processing system. 

Several industrial facilities near a residential area emit tlie inhalable pollutants ethylene oxide, polychlorobiphenyls (PCBs) and polycyclic aromatic hydrocarbons (PAHs). Tlie aimual average concentration of ethylene oxide, PCBs, and PAHs are 10 pg/in, 2 pg/m, and 5 pg/m, respectively. 

Equation (8.4) defines the average concentration, Ugut, of material flowing from the reactor. Omit the V ir) term inside the integral and normalize by the cross-sectional area, Ac = ttR, rather than the volumetric flow rate, Q. The result is the spatial average concentration a patiai, and is what you would measure if the contents of the tube were frozen and a small disk of the material was cut out and analyzed. In-line devices for measuring concentration may measure a panai rather than Uout- Is the difference important ... 

The data chain of the collected atoms can be converted to a one-dimensional composition-depth profile. The depth profile shows an average concentration of solute within the aperture, and there is always a possibility that the chemical information from the selected area is a convolution of more than one phase, as indicated diagrammatically in Figure 1.5, which represents the analysis of a FIM specimen containing second phase particles and also an interface across which there is a change of composition. 

A survey of the radon concentrations in a representative sample of more than 2000 dwellings in the UK has been completed and provisional results are now available. On average, concentrations are 29% lower in bedrooms than in living areas. The mean radon concentration weighted for room occupancy is 22 Bq m 3. Assuming an equilibrium factor of 0.35 and a mean occupancy of 75%, the mean annual exposure in UK homes is assessed as 0.08 Working Level Months (WLM) and the mean annual effective dose equivalent as 0.43 mSv. 

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