Specific-shape factor

The surface area for different species can be calculated by empirically derived equations using a species-specific shape factor, which depends on the ration of weight to height (Voisin et al. 1990). According to Voisin et al. (1990), there are several limitations in the accuracy of conversions based on body surface area (1) the surface area appears to be difficult to estimate (2) some analyses have indicated that the exponent of 2/3 may be inaccurate (3) some physiological parameters are not so well related to body surface area (4) body surface area conversions are inaccurate when the mode of administration is different across species and (5) not aU types of toxicity correlate with body surface area, e.g., skin toxicity. 

Specific Shape-Factor—The shape-factor may be defined in another way. Let there be N particles of weight w, and density p. Then the diameter of the particles is... 

The term in brackets is also a measure of particle-shape and may be termed the specific shape-factor of a particle. For spheres (a, = t, a, = 7t/6), we have a = 4.85, and for a cube a = 6. The specific shape-factor for irregular particles is usually greater than 6.0. 

A specific shape factor, is also discussed by Dallavele which can be used to describe N number of particles with a specific weight, W. Combining the density equation with Equation (77) where projection diameter, dp, is used yields. 

Then, substituting Equation (86) into the surface area equation (78) gives, where the specific shape factor, a v is now ... 

Pamies et al. [19] extended the method by dividing the inflow plane in several domains p depending on the distance from the wall. Each domain is characterized by specific shape factors, turbulent length- and time scales. Thus, the velocity fluctuation component of Eq. 1 yields... 

FIG. 17-57 Resistance factors for dust layers. Theoretical curves given are based on Eq, (20-78) for a shape factor of 0,5 and a true particle specific gravity of 2,0, [Williams, Hatch, and Greenhurg, Heat, Piping Air, Cond, i2, 259 (1940) Mumford, Markson, and Ravese, Trans, Am, Soc, Mech, Eng, 62, 271 (1940) Capwell, Gas, 15 31 (August 1.93.9)],... 

Since the Wenner rod is mechanically somewhat delicate, it is only used in loose soils or in bore holes. For all measuring rods, the specific soil resistivity is equal to the product of the measured ac resistance and the shape factor Fq, which is determined empirically. 

Also, in cases where the dimensions of a regular particle vary throughout a bed of such particles or are not known, but where the fractional free volume and specific surface can be measured or calculated, the shape factor can be calculated and the equivalent diameter of the regular particle determined from Figure 2. 

Article Exemptions. You do not have to factor into threshold or release determinations quantities of a listed toxic chemical contained In an article when that article is processed or used at your facility. An article is defined as a manufactured item that is formed to a specific shape or design during manufacture, that has end-use functions dependent in whole or in part upon its shape or design during end-use, and that does not release a toxic chemical under normal conditions of the processing or use of that item at the facility. 

Where parameter c is known as the Kozeny constant, which is interpreted as a shape factor that is assigned different values depending on the configuration of the capillary (as a point of reference, c = 0.5 for a circular capillary). S is the specific surface area of the chaimels. For other than circular capillaries, a shape factor is included ... 

Human errors may be dependent on the specific accident sequence displayed in the event tree, and, for that reason, may be included in the event tree. This requires the human-factors specialist to consider the context of the error in terms of stress, operator training in response to the accident, di.tgnosiic paiierns, environmental, and other performance-shaping factors. 

THERP (NUREG/CR-1278), is used to estimate HEPs for a risk assessment. It provides error probabilities for generic tasks and describes the process used to modify these rates depending on the specific performance shaping factors (PSFs) involved in the task... 

Many factors influence the importance of human actions in the IPEs such as plant characteristics, modeling details, sequence specific attributes, dependencies, HRA method and the >crformance shaping factors (PSFs) and the biases of both the analysts performing the HRA and... 

Product size is limited to available equipment that can handle the size and pressure as well as other processing requirements. Also involved are factors such as packaging and shipment to the customer. The ability to achieve specific shapes and design details is dependent on the way the process operates. 

In a study of the viscosity of a solution of suspension of spherical particles (colloids), suggested that the specific viscosity rjsp is related to a shape factor Ua-b in the following way ... 

Heywood gave drag curves for various values of k (H3), and tabulated the velocity correction factor (H2). Figure 6.15 shows plotted from Heywood s table. There is empirical evidence for the validity of this approach (Dl). As with sphericity, comparison for specific shapes is informative. For oblate spheroids (for which Ja is the equatorial diameter) and Re < 100,... 

Since most irregular particles of practical concern tend to be oblate, lenticular, or rod-like with moderate aspect ratio, these comparisons generally support Heywood s approach. Combining this observation with the fact that the volumetric shape factor is more readily determined than sphericity, we conclude that Heywood s approach is preferred for the intermediate range. For convenience in estimating Uj, Table 6.4 gives correlations, fitted to Heywood s values, for 0.1 < k < 0.4 at specific values of Since is relatively insensitive to interpolation for at other values of is straightforward. In common with Heywood s tabulated values, the correlations in Table 6.4 do not extrapolate to = 1 for a sphere k = 0.524). 

To obtain higher-order approximations, it is necessary to consider specific shapes. Various correction factors have been proposed for rigid spheres moving through an otherwise undisturbed fluid. The most widely used are summarized in Table 9.2. Experimental determinations of K reported by Fidleris and... 

The range of specific surface area can vary widely depending upon the particle s size and shape and also the porosity.t The influence of pores can often overwhelm the size and external shape factors. For example, a powder consisting of spherical particles exhibits a total surface area, S, as described by equation (1.6) ... 

Hence, it is supplanted by the filler density (p) and its specific surface area (Q to address the shape factors. This can successfully represent the aspect ratio effects because changes in aspect ratio are reflected in the ratio of particle surface area to particle volume, i.e., density x surface area/gram. 

The viscosity starts to increase above the CMC and it is well established that the viscosity of a colloidal solution can give information on size and shape of the particles. From studies of the viscosity as a function of micellar concentration, the intrinsic viscosity may be obtained by extrapolation. The intrinsic viscosity depends on a shape factor, and the micelle specific volume and viscosity studies are therefore used to determine micelle shape and hydration. In many cases, these factors appear to be quite constant over a wide concentration range above the CMC. In other cases, such as hexadecyltrimethylammonium bromide (Fig. 2.9), dramatic increases in viscosity are observed at higher concentrations35). Studies of surfactants with low... 

The general equation for determining specific surface involving the use of shape factors is given by Eq (16-3) above. 

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