Specific Forms

The form of the general continuity equations is usually too complex to be conveniently solved for practical application for reactor design or simulation. If one or more terms are dropped from (7.3.1.1-6) and/or integral averages over the spatial directions are considered, the continuity equation for each component reduces to that of an ideal, basic reactor type, as outlined in Section 7.2. In these cases it is often easier to apply (7.2-1) directly to a volume element of the reactor. This will be done in the next chapters, dealing with basic or specific reactor types, but in the present chapter, it will be shown how the simphfied equations can be obtained from the fundamental ones. 

It is very conunon in reactors to have flow predominantly in one direction, say, z (think of tubular reactors). The major gradients then occur in that direction, under isothermal conditions at least. For many cases, then, the cross-sectional average values of concentration (or conversion) and temperature might be used in the equations, instead of radially distributed values. The former are obtained from 

In this case, the approximation would clearly be best for highly turbulent flow, for which the velocity profiles are relatively flat. The discrepancies actually enter into the effective transport coefficients, which have to be empirically measured in any event. Another approximation concerns the reaction rate term  

1-6) becomes, after integration over the cross section. 

This last equation is simply integrated to give 

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This normal form reduces the Schodinger equation, Eq. (1), to a specific form where q remains a particle s position but x becomes a spin-like coordinate ... 

A Maclaunn series is a specific form of the Taylor series for which Xq = 0. Some standard expansions in Taylor series form are ... 

You should recognize that is just the specific form of Ks for water. The plT of a solution is now seen to be a general statement about the relative abundance of protonated solvent... 

Thermoformability is a property required by the many sheet materials used in the thermoforming industry. These properties are unique for the specific forming methods used, and are best determined by actual thermoforming tests on smaU-scale equipment. The softening or drape temperature of the material, residual stress in the sheet from its manufacture, and its melt strength and viscosity are important parameters relating to this use. 

Use of specific forms of radiant energy, infrared, ultraviolet, dielectric heating, etc., can allow specific separations to be made. The separation of clear and colored grains of glass and the separation of different metals are possible apphcations of the thermoadhesive method being considered in the field of solid-waste processing. 

All areas of the cooling water system where a specific form of damage is likely to be found are described. The corrosion or failure causes and mechanisms are also described. Especially important factors influencing the corrosion process are listed. Detailed descriptions of each failure mode are given, along with many common, and some not-so-common, case histories. Descriptions of closely related and similarly appearing damage mechanisms allow discrimination between failure modes and avoidance of common mistakes and misconceptions. 

The intent of the walkthrough inspection is to acquire a good overview of occupant activities and building functions and to look for lAQ problem indicators. No specific forms are suggested for this stage of lAQ profile development. However,... 

Gaseous corrosion is a general form of corrosion whereby a metal is exposed to a gas (usually at elevated temperatures). Direct oxidation of a metal in air is the most common cause. Cast iron growth is a specific form of gaseous corrosion in which corrosion products accumulate onto the metal surface (and particularly at grain boundaries) to the extent that they cause visible thickening of the metal. The entire metal thickness may succumb to this before loss of strength causes failure. 

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

What Is the Expected Output or Work Product. The specific form of the finished product will vaiy according to your company s practices and needs. However, it s reasonable to expect that the team s efforts will ultimately produce a set of documented Standard Operating Procedures (SOPs) for the management system, or their equivalent within your organization (see Section 6.3). Interim work products may include progress reports (see Chapter 8), documentation of discussions and analyses, flowcharts, or other materials. 

Performance-influencing factors are general conditions which increase or decrease the likelihood of specific forms of error. They can be broadly grouped into the following categories ... 

The field of nanotechnology is advancing rapidly, so it is not practical or useful to make short-term predictions about its specific form and capabilities. At most it can be noted that one of the most rapidly advancing subficlds is nanoclcctronics (sometimes referred to as molectronics, for molecular electronics). 

Since the energy shocks of the 1970s, other efforts to subsidize energy have arisen. One often-nsed justification is inadequate foresight. For example, encouraging specific forms of nonutility generation of... 

The check or specification form of Figure 4-26 is necessary and helpful when inquir)lng wire mesh entrainment uniK, either as the mesh alone, or as a complete turnkey unit including vessel. 

The conditions set forth on the Operational Checklist, Figure 7-14, are used in the example specified on the specification form (Figure 7-33). 

Figure 8-156B. Tower internals specifications form, tray type columns.

Figure 10-186. Air-cooled equipment specifications form. (Used by permission Segel, K. D. Chemical Engineering Progress, V. 55, 1959. American Insistute of Chemical Engineers. All rights reserved.)...

Installation arrangements, 351 Pump-down time, 380 Selection procedure, 374 Specification form, 377 Specifications, 373 Steam jet comparison, 356 Types of loads, 359 Ejectors, 346 Applications, 353 Barometric condenser, 249, 376 Booster, 370 Calculations Actual air capacity, 362 Air equivalent, 360... 

Lines in vacuum service, 135—141 Line symbols, 17, 23 Numbering, 23 Lined centrifugal pumps, 171 Liquid-solid particle, separators, 228 Baffle type specifications, 248 Baffle type, 247, 248 Centrifugal, 256, 259-261 Chcvron-vanc, 248, 235 Comparison chart, 230 Cyclone, 259 Specification form, 268 Vane, 259 Wire mesh, 246 York-vane, 248 Low pressure storage... 

Effects of performance changes, 201-203 Head curve for single pump, 198 Relations between head, horsepower, capacity and speed, 200 Temperature rise 207-209 Viscosity corrections, 203-207 Purging, flare stack systems, 535 Reciprocating pumps, 215—219 Flow patterns, 219 Specification form, 219 Relief areas, 437 External fires, 451, 453 Sizing, 434, 436... 

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