Approximate method, for calculating

It must be emphasized that Eq. (6.7) is only an approximate method for calculating the performance of refrigeration cycles. If greater accuracy is required, the refrigeration cycle must be followed using thermodynamic properties of the refrigerant being used. °... 

The column vapor loads (i.e. vapor flow rates up the columns) are calculated to determine the approximate equipment sizes. An approximate method for calculating the vapor flow V in a column is (Hurme, 1996). 

Hlywooi)1 f has developed an approximate method for calculating the terminal falling velocity of a non-spherical particle, or for calculating its size from its terminal falling velocity. The method is an adaptation of his method for spheres. 

There are different approximate methods for calculation of V and F . The direct variational approach [39] shows that for the 2 term of the Li-He system, the van-der-Waals attraction is overpowered by the exchange repulsion of the pa electron of M from the X core at rather large distances (R > 10 a.u.). This is substantiated by recent calculations made by Krauss [40] and Baylis [41], who demonstrated besides that for the pit electron of M, the noble-gas atom penetrates into the excited atom M until it experiences the core-core repulsion M+-X. Before the repulsion region for the A term there is net attraction that is due to the polarization of X in the field of the charged core M+. 

We discuss now approximate methods for calculation of the S matrix with the aim of obtaining more information on individual transition probabilities. 

An Approximate Method for Calculating the Efficiency of a Capillary Column... 

Another advantage of the quantum calculations is that they provide a rigorous test of approximate methods for calculating dissociation rates, namely classical trajectories and statistical models. Two commonly used statistical theories are the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and the statistical adiabatic channel model (SACM). The first one is thoroughly discussed in Chapter 2, while the second one is briefly reviewed in the Introduction. Moreover, the quantum mechanical approach is indispensable in analyzing the reaction mechanisms. A resonance state is characterized not only by its position, width and the distribution of product states, but also by an individual wave function. Analysis of the nodal structure of resonance wave functions gives direct access to the mechanisms of state- and mode-selectivity. 

Several approximate methods for calculating resonance energies and widths for atom-diatom reactive collisions are discussed. In particular, we present resonance energy calculations by semlclassical and quantal vi-bratlonally adiabatic models based on minimum-energy and small-curvature paths, by the semlclassical SCF method, by quantal SCF and configuration-mixing... 

This final method is based on the approximate methods for calculating compressible flow in a pipe, as described in Sections 6.8, 6.9 and Appendix 2, and in a valve, as described in Section 9.11.2. The major approximation made is that the specific volume of the gas in large stretches of pipework can be represented adequately by a notional average specific volume. The benefit of ASVAM is that it can be programmed to avoid implicit loops, and hence the associated problems of convergence in the main equations, while maintaining a very reasonable accuracy. 

The simplest such model is to treat DNA as a sequence of independent bases (a Bernoulli stream), each occurring with a probability equivalent to their frequency in the human genome. There are approximate methods for calculating the expected number of PQS given a certain base frequency, and the problem can be solved explicitly as well. This gives the expected density of PQS, p(PQS), as a function of p, the probability of any individual base being guanine ... 

Mansfield, M. L., Douglas, J. F., Man, S., and Kang, E.-H., Comparison of approximate methods for calculating the friction coefficient and intrinsic viscosity of nanoparticles and macromolecules. Macromolecules, 40, 2575-2589 (2007). 

We have considered in some detail several exact and approximate methods for calculation of transition probabilities (or cross sections) in colinear collisions. There exists now a great variety of other methods proposed during the last few years. Some of them will be mentioned here only briefly. 

Fig. 5.4. Specific rate functions, d,=k(E), for the two molecules of Fig. 5.3, as a function of energy above threshold. Note the minor irregularities at low energies, due to the changeover from direct count to approximate methods for calculating the state densities.

Most large centrifugal refrigeration compressors are driven by steam turbines. A gradual loss in refrigeration duty can be due to a reduction in turbine horsepower. An approximate method for calculating small changes in compressor horsepower is ... 

In spite of these complexities, several approximate methods for calculating thermodynamic properties for these types of molecule have been developed. ... 

Ametani, A. and I. Fuse. 1992. Approximate method for calculating the impedances of multiconductors with cross sections of arbitrary shapes. E/ecfr. Eng. Jpn. 111(2) 117-123. 

An approximate method for calculating the minimum reflux ratio, is given by Underwood equations. Two equations must be solved ... 

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