Graphical correlations

2 Influence of CFSE on thermodynamic data 7.2.1 Graphical correlations 

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Jet Penetration. At the high gas velocities used in commercial practice, there are jets of gas issuing from distributor holes. It is essential that jets not impinge on any internals, otherwise the internals may be quickly eroded. Figure 14 is a graphical correlation used to determine the jet penetration length as a function of gas velocity and gas density. Jets from horizontal and downflow holes are considerably shorter than those that are pointed upward. 

Figure 8-151. Graphical correlation of sieve tray ultimate capacity for hydrocarbons. Used by permission, Capps, R. W., The American Institute of Chemical Engineers, Chem. Eng. Prog. V. 89, No. 3 (1993), p. 35, all rights reserved.

Weber (Wl) has reported measurements of gas holdup for the experimental system described in Section V,B,4. The following empirical relationships can be derived from the graphical correlations ... 

Kato (K3) measured so-called critical gas velocities corresponding to the complete suspension of solids, and presents a graphical correlation of the results for glass spheres (diameters from 0.074 to 0.295 mm), magnetite particles (particle size from 0.038 to 0.175 mm), and sand particles (particle size 0.147 to 0.295 mm). 

E0so is measured in electrochemistry and is usually known with an accuracy to 0.01 V or better.8 On the other hand 0 is measured with surface physics techniques that have an accuracy of 0.05 eV, rarely better and often worse (because of imperfect surfaces)/9 Thus, Eq. (28) does not ensure an appropriate accuracy for AX, so that the uncertainty may outweigh the value itself. The best way to proceed is to plot E0=q vs. 0 for a number of metals and to derive information about AX from eventually recognizable graphical correlations using statistical analysis. 

It is known from many publications that aeration reduces the Ne number as a result of the formation of gas cavties behind the stirrer blades. The measured values can be described with sufficient accuracy using the following graphic correlation [23] ... 

For a flow boiling crisis, an empirical scaling factor was suggested by Stevens and Kirby (1964). It is a graphical correlation developed from uniform-flux round-tube data. They suggested an empirical function ... 

The graphical correlation shown in Figure 5.30 was originally developed for a steam-water mixture of high quality. Coffield et al. (1967) extended its validity into the subcooled region by comparing their subcooled Freon-113 DNB data with... 

A graphical correlation for this, based on the friction factor, is given by Perry et al. (1984, p. 5-24), together with values of e. This can be used in conjunction with equation 15.4-2 to determine D, and hence L, by means of the following algorithm ... 

The ratio of wake volume to bubble volume is difficult to assess, and is given by Kunii and Levenspiel (1991, p. 124) in the form of graphical correlations with particle size for various types of particles. From this, we assume that the bed fraction in the wakes1 is ... 

Conventional pipeline calculations in which "dry" hydrocarbon flashes are performed to determine the hydrocarbon liquid formation the liquid water condensed is estimated using one of the available natural gas water content charts (1, 15), and the Hammerschmidt equation (11) and a graphical correlation are used to... 

The conventional technology of pipeline calculations does not normally predict the carbon dioxide or hydrocarbon content of the water rich phase. These can be estimated by other graphical correlations. 

Both "wet" flash calculations predict a higher concentration of water in the vapor phase than the graphical correlations. The presence of methanol reduces the predicted water content of the vapor phase. 

The final graphical correlation given by the authors is in terms of the following two groups ... 

A useful graphical correlation for flooding rates was first presented by Sherwood et a/.(60) and later developed by Lobo el al.(6l> for random-dumped packings, as shown in Figure 4.17 in which ... 

B31. Buchthal, F., Svensmark, O., and Schiller, P. J., Clinical and electroencephalo-graphic correlations with serum levels of diphenylhvdantoin. AM A Arch. Neurol. 

For bubbles and drops rising or falling freely in infinite media it is possible to prepare a generalized graphical correlation in terms of the Eotvds number, Eo Morton number, M and Reynolds number. Re (Gl, G2) ... 

The graphical correlation is presented in terms of the perimeter equivalent factor Yj sed in Figs. 4.9 and 4.10. The points have been calculated for axisymmetric shapes. 

The generalized graphical correlation presented in Fig. 2.5 gives one method of estimating terminal velocities of drops and bubbles in infinite liquid media. For more accurate predictions, it is useful to have terminal velocities correlated explicitly in terms of system variables. To obtain such a correlation is especially difficult for the ellipsoidal regime where surface-active contaminants are important and where secondary motion can be marked. 

In the absence of a fundamental understanding, the prediction of froth density relies on empirical correlation. Figure 6.3-1 shows a simple graphical correlation of mean downcomer froth density as a function of the density difference between liquid and vapour. Brierley [1] indicates that the correlation was produced from relatively few data. Therefore, it is preferable to obtain a value from operating data close to flooding on the same system. 

At high liquid rates droplets tend to be reentrained and the pad may become flooded. Some data obtained by Poppele (1958) are cited by York (1983, p. 194). A graphical correlation credited to the Fluor Co. is represented by Branan (1983, p. 67) by the equation... 

For arithmetic calculations and graphical correlation, it is useful to define the term ... 

The isoelectric point may be conveniently defined as the ZPC expected for a pure, single component solid oxide, hydrous oxide, or hydroxide with a nondefective structure in an electrolyte totally devoid of specifically adsorbed polar or ionic species. An IEP(s) can be calculated from the charge and size of the cation using Equation 13 and the constants in Tables I and II. The maximum accuracy to be expected may be judged from the graphical correlation given in Figure 3. 

By using the laboratory data described and presented above, particularly the graphical correlations, and making some engineering assumptions, material balances for a sea water conversion plant using the ammonium bicarbonate ion exchange process were then developed. 

Finally, a fourth class of alkaloids has been discovered, apparently specific to the leaves of P. Lyallii (57). It consists of two unseparable products, 37 and 38, in the ratio 2 to 1, which readily give lyaloside (23) on mild methanolysis, along with two esters, namely, methyl ferulate and methyl sinapate (39 and 40, respectively). Elucidation of their structure was essentially based on NMR considerations (57). Graphical correlations between 1H- and 13C-NMR spectra, associated with analysis of the residual constant coupling during a step by step [200 Hz per 200 Hz from 0 (TMS) to 2000 Hz] off-resonance procedure, permitted the precise assignment of all the carbon atoms of the products (58). 

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