Averaged area geometric-mean

This means that the average permeability for this heterogeneous medium is the area-weighted average of the average permeability of each of the elements. If the permeability of each element is log-normally distributed, these are the geometric means. 

Exposure Route/Concentrations/Durations Inhalation/geometric mean exposure of <1 ppm (range, 0.01-3.3 ppm personal samplers), up to 6 ppm (area samples)/mean service years, 16.5 (Leeser et al. 1990) Inhalation/average exposure 8 ppm/5-15 y (El Ghawabi et al. 1975) Inhalation/5 ppm/unknown/(Grabois 1954 Maehly and Swensson 1970 Hardy et al. 1950). ... 

Another popular technique for obtaining an average diameter based on surface area consists of calculating the diameter of a hypothetical droplet whose surface area is equal to the total surface area of the spray divided by the total number of droplets in the spray. An average of this type may be expressed as a geometric mean of an appropriate set of distribution moments. 

Eq (3-7) represents the summation of the surface-areas divided by the summation of the diameters. It gives a mean based on the surface observed, and the volume or total surface of the particle does not enter into the calculation. As an average it is comparable to the arithmetic and geometric means. 

From these equations we see that once the geometric-mean size and the standard deviation are determined, we are in position to compute the diameter of a particle having an average surface area and an average volume. Hatch and Choate tested these equations and found general agreement with laboratory measurements. 

Once there is a measure of the concentration of the pesticide in the exposure medium (air, water, food, etc.) in contact with the body or the actual concentration that comes into contact with the body, a daily dose metric can be calculated (e.g. maximum, average, geometric mean, etc.). This typically involves developing a mathematical equation that expresses dose as a function of pesticide concentration and other important parameters referred to as human exposure factors (USEPA, 1999a). In the context of this discussion, the term human exposure factor refers specifically to (a) human characteristics, such as body weight, surface area, life expectancy, inhalation rates for air and consumption rates for food, drinking water and soil (b) human behaviors, such as activity patterns, occupational and residential mobility and consumer product use, which are used by exposure assessors to calculate potential dose. 

The average area Am is given by the average of both surface areas A t = A(rx) and j = A(r2). One gets the arithmetic mean for the flat plate, the logarithmic mean for the cylinder and the geometric mean for the sphere. It is known that... 

It should be noted that the "average" plasma concentration, obtained by employing Eqs 11.15 or 11.17, is neither the arithmetic nor the geometric mean of maximum and minimum plasma concentrations at infinity. Rather, it is the plasma concentration at steady state, which, when multiplied by the dosing interval, is equal to the area under the plasma concentration-time curve (AUC)o (i.e. from f=0 to t r). 

Estimated areas were normalized by the averaging method. The values presented in this table are geometric means. 

In Tables III and IV are listed the values of the average size of the dispersed particles (S) for the PS/PMMA specimens from our earlier work and the PS/P(MMA-S) specimens under consideration here, respectively. The average size is defined, perhaps somewhat arbitrarily, as the average of the geometrical mean diameter of the particles in a given representative area. Some care must be taken to avoid obtaining underestimates of S (39) usually the standard deviation of our values is within 5%, and never greater than 10%. 

For the following particle size distribution data, calculate the arithmetic mean, geometric mean, count median, and diameter of the particle with average surface area. 

Similarly, the geometric surface mean diameter, D s, is defined as the average diameter weighted according to the surface areas Sj in the various groups ... 

Other possible geometrical diameters can be used to determine the mean particle diameter of a polydisperse system. Examples are the surface average, ds, and volume average diameters, dv where ds is defined as the diameter of a sphere having the same surface area as the particle and dw is the diameter of a sphere having the same volume as the particle. These are given by ... 

---