Empirical methods, for estimating

The two most frequently used empirical methods for estimating the stage requirements for multicomponent distillations are the correlations published by Gilliland (1940) and by Erbar and Maddox (1961). These relate the number of ideal stages required for a given separation, at a given reflux ratio, to the number at total reflux (minimum possible) and the minimum reflux ratio (infinite number of stages). 

The method preferred in our laboratory for determining the UWL permeability is based on the pH dependence of effective permeabilities of ionizable molecules [Eq. (7.52)]. Nonionizable molecules cannot be directly analyzed this way. However, an approximate method may be devised, based on the assumption that the UWL depends on the aqueous diffusivity of the molecule, and furthermore, that the diffusivity depends on the molecular weight of the molecule. The thickness of the unstirred water layer can be determined from ionizable molecules, and applied to nonionizable substances, using the (symmetric) relationship Pu = Daq/ 2/iaq. Fortunately, empirical methods for estimating values of Daq exist. From the Stokes-Einstein equation, applied to spherical molecules, diffusivity is expected to depend on the inverse square root of the molecular weight. A plot of log Daq versus log MW should be linear, with a slope of —0.5. Figure 7.37 shows such a log-log plot for 55 molecules, with measured diffusivities taken from several... 

A semi-empirical method for estimating the detonation velocities of explosives composed of C, H, N, and O atoms has been proposed.PI The heat of detonation per mole, AHd, defined by... 

Introduction. During the past decade there have been significant developments of empirical methods for estimating the thermodynamic, properties of organic compounds based on group additivity methods... 

Empirical Method for Estimating the Binding Affinity of a Protein-Ligand Complex. 

A conclusion that may be drawn on this section is that the empirical methods for estimates of the correlation energy may be profitable in applications and that their further development is worth pursuing, It should be realized that for molecules that are (by their size) of interest to chemists, they mostly represent the only feasible approach. 

Kopp s rule is a simple empirical method for estimating the heat capacity of a solid or liquid at or near 20°C. According to this rule, Cp for a molecular compound is the sum of contributions (given in Table B.IO) for each element in the compound. For example, the heat capacity of solid calcium hydroxide. Ca(OH)2, would be estimated from Kopp s rule as... 

R. Wang, L. Liu, L. Lai, and Y. Tang. SCORE A new empirical method for estimating the binding affinity of a protein-ligand complex. Journal of Molecular Modelling, 4 379-394, 1998. 

The most commonly used empirical method for estimating the permeability, however, is the "permachor" method of Salame [21,74-78]. An additive property, which is called the permachor and represented by the Greek letter n, is defined, and P is expressed in terms of n. The values of 7t are obtained empirically, and are assumed to quantify the key physical factors believed to determine the permeabilities of polymers, namely their cohesive energy densities and their fractional free volumes. The P s (in DU) of a large number of polymers to 02, N2 and... 

For some elements with varying oxidation states, series of oxoacids with different numbers of oxygen atoms may exist (Table 6.3). There is no adequate thermodynamic treatment for rationalizing the observed trends within a series, but there are certain empirical methods for estimating X. The best known of these is Bell s rule (equation 6.31) which... 

Because devices with this kind of flow are widely used in distillation and absorption, the empirical methods for estimating their performance are summarized in books on those topics [7]. 

Ginsberg, A. P, Miller, J. M. (1958). An empirical method for estimating the electron affinities of atoms. J. Inorg. Nucl. Chem. 7(4), 351-367. 

The capillary bundle approach has also been extended for correlating data on pressme drop in packed beds of spherical particles in the transitional and turbulent regions. Both Mishra et al. [1975] and Brea et al. [1976] proposed the following empirical method for estimating the effective viscosity , fies ... 

The organization responsible for installation of the rectifier system, whether it be the operating company itself or an outside design contractor, probably will lack knowledge of the overall power supply situation. Therefore, most electric utility authorities will propose standard empirical methods for estimating the effects of a proposed new installation. In the final analysis, however, measurements must be made on the operating system. Harmonic filters can be installed to compensate for the problem, but in the real world it may later be found that these must be adjusted to cater for unforeseen conditions. 

It is felt that the analytical method presented here is distinctly superior to any of the empirical methods for estimating gas consumption, such as the so-called "saturation rule." Application of the analytical method, however, is somewhat more difficult. The method should be suitable for all tank systems that use cryogens (such as hydrogen, oxygen, nitrogen, fluorine, carbon monoxide and neon) and that are equipped with a gas diffuser to prevent direct jetting of the gas into the liquid. In addition, the method is set up so that large variations in system operation may be incorporated by a person reasonably well versed in the principles of thermodynamics and heat transfer. 

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