Correlation line

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Power consumption for impellers in pseudoplastic, Bingham plastic, and dilatant nonnewtonian fluids may be calculated by using the correlating lines of Fig. 18-17 if viscosity is obtained from viscosity-shear rate cuiwes as described here. For a pseudoplastic fluid, viscosity decreases as shear rate increases. A Bingham plastic is similar to a pseudoplastic fluid but requires that a minimum shear stress be exceeded for any flow to occur. For a dilatant fluid, viscosity increases as shear rate increases. 

The kinetics of the hydrolysis of some imines derived from benzophenone anc primary amines revealed the normal dependence of mechanism on pH with ratedetermining nucleophilic attack at high pH and rate-determining decomposition of the tetrahedral intermediate at low pH. The simple primary amines show a linear correlation between the rate of nucleophilic addition and the basicity of the amine Several diamines which were included in the study, in particular A, B, and C, al showed a positive (more reactive) deviation from the correlation line for the simple amines. Why might these amines be more reactive than predicted on the basis of thei ... 

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

Tank Configuration Slope X of Correlation Line Reference... 

Althou sufficient data to provide thorough tests of mechanism are lacking, it is possible to make some tentative conclusions. Sets 15-67, 15-69, and 15-71 give highly significant correlations with eq. (30). These sets include both monosubstituted and disubstituted dienophiles. Obviously, then, both mono-substituted and disubstituted dienophiles lie on the same correlation line and have the same values of a and 3. It therefore seems likely that these sets undergo a concerted mechanism. 

This theory appears not to involve adjustable parameters (other than the nuclear radius parameters that were taken from the literature). In particular, it was criticized that the calibration approach involved a slope that is too high by about a factor of two. However, in actual calculations with the linear response approach, it was found that the slope of the correlation line between theory and experiment (dependent on the quantum chemical method) is close to 0.5. Thus, it also requires a scaling factor of about 2 in order to reach quantitative agreement with experiment. The standard deviations between the calibration and linear response approaches are comparable thus indicating that the major error in both approaches still stems from errors in the description of the bonding that is responsible for the actual valence shell electron distribution. 

Based on an extrapolation of the correlation line for ArCOCH3 + NH2OH. 

NMR interpretation has made significant advances with diffusion-editing pulse sequences and two-dimensional inversion of diffusivity and T2 relaxation [7,40-44]. The 2D inversion can also be used to compare Tj and T2 relaxation with each other [42]. Distributions of these two characteristic parameters can now be displayed on a 2D map and the relationship between them more easily visually interpreted. The 2D distribution map can be interpreted by comparing the measured distribution with the line for the bulk diffusivity of water and the correlation lines for the hydrocarbon components in crude oils, shown in Figure 3.6.10 as dashed lines [40-46]. Figure... 

Figure 5.12 Glide activation energies from high temperature data vs. energy band gaps. Note that the data for the homopolar crystals (C, SiC, Si, and Ge) lie quite close to the correlation line, while the data for The heteropolar crystals show some scatter. The reason why GaP Is an exception is not known. Also, note that the slope of the correlation line is two. 

Figure 6.2 shows yield stress versus shear modulus data for face-centered cubic metals at about 78 K. The yield stresses were derived from Brinell Hardness Numbers (Gilman, 1960). The slope of the correlation line is tb = G/333, in good agreement with the theoretical estimate of the previous paragraph. 

The structures of the prototype borides, carbides, and nitrides yield high values for the valence electron densities of these compounds. This accounts for their high elastic stiffnesses, and hardnesses. As a first approximation, they may be considered to be metals with extra valence electrons (from the metalloids) that increase their average valence electron densities. The evidence for this is that their bulk modili fall on the same correlation line (B versus VED) as the simple metals. This correlation line is given in Gilman (2003). 

Equation 16.12 expresses a relation between q and B.This is not a universal relation, but it does apply to the sp-bonded elements of the first four columns of the Periodic Table. Using chemical hardness values given by Parr and Yang (1989), and atomic volumes from Kittel (1996), it has been shown that the bulk moduli of the Group I, II, III, and IV elements are proportional to the chemical hardness density (CH/atomic volume) (Gilman, 1997). The correlation lines pass nearly through the coordinate origins with correlation coefficients, r = 0.999. Thus physical hardness is proportional to chemical hardness (Pearson, 2004). 

The fit of the data to the correlation line indicates that the relative yields of 27Al and s ifg secondary ions are constant over the compositional range anorthite 100 to anorthite 50. The slope of the line, O.S1, reflects the higher sensitivity of the ion probe for Mg, and is used to convert measured secondary ion ratios to elemental ratios. 

Three distinct nebular phenomena can in principle contribute to the discordant Mg isotopic systematics late formation of individual anorthites followed by gentle compaction of B2 inclusions, selective secondary alteration of anorthites after inclusion formation, and initial heterogeneities in 26A1 similar to those observed in stable isotopes. The fact that data from anorthites in both B2 inclusions are used to construct the two new Al-Mg correlation lines suggests that whatever processes(es) or... 

Fortunately, if enough samples are available from a given aquifer, the variations of 2H and 180 can be compared with Craig s empirical relationship, which for normal surface waters is 62H = 8 6180 + 10°/oo. Large departures from Craig s correlation line could indicate the effects of evapotranspiration or of hydrothermal reactions. 

There would seem to be two positions one can take with respect to the interpretation of the behavior revealed by Figs 1 and 2. The first, which would undoubtedly be favored by proponents of HSAB, is that the large deviations of the points for soft-base nucleophiles in Fig. 2 show that HSAB considerations do play an important role in determining the relative order of reactivity of a series of nucleophiles in nucleophilic substitutions at different electrophilic centers when those centers differ significantly in their degree of hardness , and that the failure to observe sizeable deviations from the correlation line in Fig. 1... 

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