Correlation factors

Koch/Sul2er SMX has a correlation factor for design based onlog(viscosity ratio of the two Hquids). 

It is not always necessaiy to use all of the terms in the correlating factor, and those conditions which are held constant throughout the testing may be dropped from the correlating factor. Many times, air rate data are not av able and reasonable correlations can be obtained... 

Smith uses settling height as a correlating factor which is intended for use with various tray types. The correlation is shown in Figure... 

Smith" uses settling height as a correlating factor, which is intended for use with various tray types. The conrelation is shown in Figure 1. Curves are drawn for a range of settling heights from 2 to 30 inches. Here, U is the vapor velocity above the tray not occupied by downcomers. 

DEL = Column flooding correlating factor FPL = Tray flow path length, ins. 

The contiguity factor, Cj is actually a so-called fudge factor used to make sense out of the comparison of experimental dataTwitlirtheore-tical predictions. This correlation factor is useful only when the data fall between the theoretical bounds. The concept of a contiguity factor, i.e.. 

The correlation factor, k, is a function of the liquid drop size, liquid viscosity, liquid load, disengaging space, type of mesh weave, etc. k varies somew hat with system pressure as pressure increases the k value decreases. The manufacturers should be consulted for final design k valves for a sys-... 

Correlating factor for viscous flow power, Table 5-1 Mixing factors, turbulent flow power. Table 5-1 Viscosity correction factor for turbulent How (static mixer)... 

Correlating factor for turbulent flow power Weber number... 

E = superficial liquid entrainment rate, Ib/hr/ff Fj, Fj = correlation factors defined by equations... 

For systems containing three or more electrons very little is so far known about the foundation for the method of correlated wave functions, and research on this problem would be highly desirable. It seems as if one could expect good energy results by means of a wave function being a product of a properly scaled Hartree-Fock function and a correlation factor" containing the interelectronic distances ru (Krisement 1957), but too little is known about the limits of accuracy of such an approach. 

The results show that it is possible to improve the Hartree-Fock energy —2.86167 at.u. considerably by means of a simple correlation factor, but also that it is essential to scale the total function W properly to fulfil the virial theorem. The parameters in the best function u of the form of Eq. III. 121 are further given below ... 

We note that it is possible to combine the method with correlation factor with the method using superposition of configurations to obtain any accuracy desired by means of comparatively simple wave functions. For a very general class of functions g(r12), one can develop the quotient (r r2)lg(r12) according to Eq. III.2 into products of one-electron functions y>k(r), which leads to the expansion... 

In Section II.D(4c), it was pointed out that, in treating correlation effects in a molecular system, it is of essential importance that the improved wave function leads to an energy curve having correct asymptotic behavior for separated atoms. It has been shown (Frost, Braunstein, and Schwemer 1948) that this condition may be fulfilled by a convenient choice of a correlation factor g. Let us consider the H2 molecule and a wave function of the type... 

The function g(r j) is here a correlation factor, and it is clear that, if this function is chosen in different ways, we will have different coefficients CK in the expansion in the first factor. An important problem is then to try to find forms of the correlation factor which will reduce this expansion as much as possible, and a particular problem is to investigate how good an approximation could be obtained by a single determinant ... 

The main advantage of the method with correlation factor, based on Eq. III. 128 or Eq. III. 129, lies in the fact that it may be applied to any many-electron system. The practical calculation of the energy integrals involved may be fairly cumbersome, but the approach is nevertheless straightforward. 

This analysis shows that a refinement of the Hartree-Fock method by means of a correlation factor g(r12> rlz, r2Z,. . . ) seems to be possible along several lines, but the numerical work involved... 

In Section III.E(2) we discussed the improvement in the con-vergency of expansion III. 18 which could be obtained by introducing a suitably chosen correlation factor g(r12, r13, r23,. . . ), and it is clear that a similar procedure can be carried out also in connection with Eq. III. 142, provided that the factor g does not change the symmetry character of the wave function. In complete analogy with Eq. III. 128, we hence obtain... 

Again it is an important problem to find such forms of the correlation factor g as will reduce the expansion over the ordered configurations K as much as possible. We will also consider the ap-... 

The data show that, in the case of the He-like ions, a combination of the method using correlation factor and the method with different orbitals for different spins leads to excellent results. 

The convergency of expansion IV.3 may also be improved by introducing a correlation factor g ... 

Bohm-Pines" plasma model seems at first sight to be very different from the expansion methods treated here, but in Section III.E(2b) it was shown that it is rather closely connected with the method using correlation factor. Similar to Wigner s formula, it probably gives reasonable values for the correlation energy for the... 

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