Generalization Justifiable

A short dissertation upon almost any extensive subject such as this subject is usually blessed by the reader s understanding that generalizations are not only justifiable but also mandatory in order to cover the scope of the subject. However, a learned treatise of ponderous bulk can be readily exempted from criticism for tedious passages devoted to details in that the authors are attempting to present a full and uncompromised assay of the subject. Somewhere in between lies this 

Available shapes Available sizes Available surface texture Manufacturing tolerances 

Crystallinity Molecular weight Flammability Spatial configuration Chemical resistance 

Tensile properties Heat distortion Compression strength PV Limit Toughness 

Tensile properties Compression strength Fracture toughness Hardness 

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For draining principal items of process equipment, level-controUed condensate chambers provide much better performance and rehabiUty than steam traps. Usage is generally justified when condensate flow is greater than 4500 kg /h. 

For all the results presented, the contribution of SIMS is seen as being semi-quantitative. A more exhaustive interpretation of the results in terms of quantification is not generally justified. 

We shall now see that, if a few (generally justified) approximations hold, such an approach is quite possible. 

The representation of a four-dimensional function by a superposition of functions of smaller dimension is not generally justified. However, in extreme cases, at very small values of one of the parameters, the dependence on it can be negligible. For instance, under condition (10.76)... 

For a density ratio of 2 the Reynolds number will be less than 1 for spherical particles with radii less than about 75 p,m. We are therefore generally justified in neglecting inertia effects for the particle range of interest. 

From the above considerations we can now define what is meant by electrically neutral solutions. If the dimensions of the system L are much larger than Aj3, then whenever local charge concentrations arise or external potentials are introduced into the solution they are shielded out in a distance short compared with L, leaving the bulk of the solution free of large electric potentials or fields. Based on a Debye length of 1 to 10 nm, the assumption of electrical neutrality is generally justified for the problems so far considered. However, as we shall discuss in the next section, in the case of very small charged microscopic capillaries, such as are characteristic of membranes and finely porous media, the double layer is central to the calculation of the solute and ion fluxes. 

Comments The calculation demonstrates that the approximations in Raoult s law are generally justified for pressures around ambient. 

The assumptions underlying the choice of this type of kinetics arc negligible effect of the reverse reaction as well as pseudoconstant values of concentrations of some of the other components and also of the homogeneous catalyst. Only the latter is generally justified. Hence, first-order kinetics is a crude approximation which can only be applied over certain ranges of concentration with different rate constants applying to different locations in the column. 

This equation can also be derived by formally applying the lAST, using the Sips equation, Eq. (47), to describe pure component data. Hence, for adsorption of gas mixtures onto activated carbon, the use of Eq. (50) is generally justified. 

The barrier properties of polymer/layered silicate nanocomposites are generally justified and theoretically treated by considering models geometrically based like the "tortuous path," that is, when impermeable nanoparticles are incorporated into a polymer, the permeating molecules are forced to wiggle around them in a random walk, and hence diffuse by a tortuous pathway. 

In the United States it is common medical practice to supplement infant formula with iron sometime during the first year of life because human milk is virtually devoid of iron. Given what is now known about iron metabolism by bacteria, many research workers in nutrition believe that iron supplementation is not generally justified or wise. 

Partial lead pipe replacement of the public portion of the lead service lateral is being practiced in some cities. As found in recent US studies (AWWARF, 2008), partial lead pipe replacement is only a marginal strategy for controlling lead concentrations in drinking water at tap outlets. It is generally justified by reducing the liability of the water supplier for lead emissions from domestic pipes. 

To date, no analogous results on wall effects are available in non-Newtonian liquids. Some workers (De Kee et al., 1986 Miyahara and Yamanaka, 1993) have minimized wall effects [on the basis of Eq. (16)], whereas others (Calderbank et al., 1970) have corrected their data using Eq. (16). Yet others (Acharya et al., 1977 Haque et al., 1988) have altogether ignored wall effects. Clearly, neither of these procedures is generally justifiable. Based on the behavior of rigid particles (Chhabra, 1993), one can perhaps conjecture that the wall correction is likely to be smaller in non-Newtonian media than in Newtonian liquids. Finally, it should be borne in mind that a 10% error in velocity will lead to a 20% error in drag coefficient ... 

Equation (2.8.8) is a quadratic equation in which may be solved to find /in its dependence on X2- However, with all of the above approximations, we are generally justified in neglecting the quadratic term in ( //7/). Equation (2.8.8) may then be inverted to read... 

It should be noted that in using Eqs. (5) or (7) to describe the nucleation frequency we have assumed a steady-state concentration of subcritical embryos and have ignored the effect of transients during which such concentrations are established. Such neglect is generally justified whenever the time required to establish the steady-state nucleation rate is small relative to the total transformation time and to the time scale of the experiment—conditions which may not be fulfilled for some transformations in condensed phases. 

What these authors actually did was to n lect the second term on the t%ht-hand side of Eq. (23) on the basis that a is usually very large compared with unity. This simplification fe not generally justified because... 

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