Similarity analyses

Criticality in the above example is set in the context of guaranteeing production. However, a similar analysis will be performed with respect to the criticality of guaranteeing safety and minimum impact on the environment. 

A similar analysis for fluorination of methane gives AH° = -426 kJ for its heat of reaction Fluori nation of methane is about four times as exothermic as chlorination A reaction this exothermic if it also occurs at a rapid rate can proceed with explosive violence... 

Simila.rityAna.Iysis, Similarity analysis starts from the equation describing a system and proceeds by expressing all of the dimensional variables and boundary conditions in the equation in reduced or normalized form. Velocities, for example, are expressed in terms of some reference velocity in the system, eg, the average velocity. When the equation is rewritten in this manner certain dimensionless groupings of the reference variables appear as coefficients, and the dimensional variables are replaced by their normalized relatives. If another physical system can be described by the same equation with the same numerical values of the coefficients, then the solutions to the two equations (normalized variables) are identical and either system is an accurate model of the other. 

The principal difficulty faced by the experimenter in applying the results of dimensional or similarity analysis is that often there is insufficient... 

A similar analysis can be carried out for any axisymmetric tube to yield ... 

A typical microbiological analysis in a troubled carbon-steel service water system is given in Table 6.2. Table 6.3 shows a similar analysis for a cupronickel utility main condenser that showed no significant corrosion associated with sulfate reducers. When biological counts of sulfate reducers in solid materials scraped from corroded surfaces are more than about 10, significant attack is possible. Counts above 10 are common only in severely attacked systems. 

We can perform a similar analysis for plastic yielding. A panel with the section shown in Fig. 27.5 yields at a load... 

Figure 1 shows a positive static SIMS spectrum (obtained using a quadrupole) for polyethylene over the mass range 0—200 amu. The data are plotted as secondary ion intensity on a linear y-axis as a function of their chaige-to-mass ratios (amu). This spectrum can be compared to a similar analysis from polystyrene seen in Figure 2. One can note easily the differences in fragmentation patterns between the...

A similar analysis of the 1,5-sigmatropic shift of hydrogen leads to the opposite conclusion. The relevant frontier orbitals in this case are the hydrogen Is orbital and ij/j of the pentadienyl radical. The suprafacial mode is allowed whereas the antarafacial mode is forbidden. The suprafacial shift corresponds to a favorable six-membered ring. 

A similar analysis can be done for the curved surface of an essentially spherical particle that contains asperities. Let us assume that all the asperities are the same size. Initially, no more than three asperities on the particle can contact the presumably smooth surface. As the asperities compress under the applied load, more asperities, that are situated further away from the substrate due to the curvature of the particle s surface, come into contact. These are the first to separate from the substrate upon application of a detachment force. In essence, detachment occurs by breaking the contacts between the asperities and the contacting surface, one at a time. 

By a similar analysis it may be shown that, for applied stresses (rather than applied strains) in the global directions, the overall compliance matrix [5] has the form... 

When the polymer melt emerges from a die with a rectangular section there will be swelling in both the width (T) and thickness (H) directions. By a similar analysis to that given above expressions may be derived for the swelling in... 

By similar analysis it may be shown that for a short rectangular slit the swelling ratios in the width (T) and thickness (//) directions are given by... 

Kuhl, A. L. 1983. On the use of general equations of state in similarity, analysis of flame-... 

We perform a similar analysis procedure for each excited state for the two basis sets. Here are the final results of the two jobs, along with the corresponding experimental excitation energies ... 

Obtain the energy for axial methylcyclohexanone, and use equation (1) to calculate the room temperature equilibrium distribution of equatorial and axial conformers. Is the amount of the axial conformer significant (>5%) Perform a similar analysis as above and decide which face of the carbonyl in the axial conformer is more likely to undergo nucleophilic attack. Does addition lead to the same alcohol as before ... 

The off-diagonal terms (i j) are treated to a similar analysis. Each penetration term involving different basis functions that are on the same atomic centre are given a value of — Vab to maintain invariance. Suppose now that Xi is centred on nucleus A and Xj on nucleus B. We have... 

For purposes of this specification, stresses in the individual members of a latticed or trussed structure resulting from elastic deformation and rigidity of joints are defined as secondary stresses. These secondary stresses may be taken to be the difference between stresses from an analysis assuming fully rigid joints, with loads applied only at the joints, and stresses from a similar analysis with pinned joints. Stresses arising from eccentric joint connections, or from transverse loading of members between joints, or from applied moments, must be considered primary stresses. 

Dukler, A. E. et al., Frictional Pressure Drop in Two-Phase Flow1 B—An Approach Through Similarity Analysis, A.I.Ch.E.J. 10,... 

Alike any other G-protein coupled receptors (GPCRs), mGlu receptors have seven transmembrane helices, also known as the heptahelical domain (Fig. 2). As observed for all GPCRs, the intracellular loops 2 and 3 as well as the C-terminal tail are the key determinants for the interaction with and activation of G-proteins. However, sequence similarity analysis as well as specific structural features make these mGlu receptors different from many other... 

A similar analysis can be made in terms of a space average24 over a region whose size is of the order of a molecular diameter.) Integrating Eq. (1-121) over all particles except the first ... 

Substrate titration. Imagine that the two straight-line portions of Fig. 6-1 were allowed to intersect. What is the significance of the intersection pH Show that the value of log k, at the intersection point is 0.301 units smaller than log ( W- Conduct a similar analysis of Fig. 6.1 b. 

One of the most Important thermophysical properties of reactor fuel In reactor safety analysis Is vapor pressure, for which data are needed for temperatures above 3000 K. We have recently completed an analysis of the vapor pressure and vapor composition In equilibrium with the hypostolchiometric uranium dioxide condensed phase (1 ), and we present here a similar analysis for the plutonium/oxygen (Pu/0) system. 

Application of equation 10 to the experimental D vs. [HSOIJ] data determined at 25°C and both 1 and 2 M acidity yielded straight line plots with slopes indistinguishable from zero and reproduced the Bi values determined in a non-linear regression fit of the data. This result implies no adsorption of PuSO by the resin and justifies use of the simpler data treatment represented by equation 2. A similar analysis of the Th(IV)-HSOiJ system done by Zielen (9) likewise produced results consistent with no adsorption of ThS0 + by Dowex AG50X12 resin. 

For an ideal gas in non-isothermal flow. If the pressure and volume are related bv Pi — constant, then a similar analysis gives ... 

A complete description of the effects of a crystal field upon a d" ion would include similar analysis of the behavours of all terms arising for that d" configuration. Box 3-7 summarizes the case for d, and in Box 3-8, we illustrate a method of using Fig. 3-19 to determine Dq and B values from real spectra. 

A similar analysis of [1,5] sigmatropic rearrangements shows that in this... 

From a similar analysis by Marsden and Smith using all the spectroscopic data available in 1989 the following equilibrium structure was derived [27] ... 

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