Velocity correlation coefficients calculation

The parameter reflects interactions of the cation-constituent with the solvent and with itself. 1 likewise for the anion-constituent, while 1 is a measure of the degree of coupling between the motions of cation- and anion-constituent. The 1 approach has been most actively fostered by Don Miller (TtO 111. 115). An alternative method of representation, introduced by Gerhard Hertz (116.1171, is based on velocity correlation coefficients. There are six of these for a binary electrolyte with self-diffusion coefficients being required to evaluate them. Sets of vcc values have recently been published for concentrated solutions of electrolytes which exhibit strong complexation like Cdl (118). The main problem in calculating these turned out to be a deficiency in suitable transference number information ... 

I quantities x and y are different, then the correlation function js sometimes referred to ross-correlation function. When x and y are the same then the function is usually called an orrelation function. An autocorrelation function indicates the extent to which the system IS a memory of its previous values (or, conversely, how long it takes the system to its memory). A simple example is the velocity autocorrelation coefficient whose indicates how closely the velocity at a time t is correlated with the velocity at time me correlation functions can be averaged over all the particles in the system (as can elocity autocorrelation function) whereas other functions are a property of the entire m (e.g. the dipole moment of the sample). The value of the velocity autocorrelation icient can be calculated by averaging over the N atoms in the simulation ... 

Other orientational correlation coefficients can be calculated in the same way as tf correlation coefficients that we have discussed already. Thus, the reorientational coiTelatio coefficient of a single rigid molecule indicates the degree to which the orientation of molecule at a time t is related to its orientation at time 0. The angular velocity autocorrelatio function is the rotational equivalent of the velocity correlation function ... 

Drag coefficient Q/l. .Re) is the drag coefficient calculated using the correlation for subsonic flow with Ma=l. f V/1.75, Re ) is the drag coefficient calculated using the correlation for supersonic flow with Ma00=1.75 Mach number based on relative velocity between gas and sphere ... 

Diffusion coefficients can be calculated directly from the velocity correlation functions or from mean square displacements, as ... 

Time correlation functions can be used in conjunction with the Green-Kubo relations to calculate the various transport coefficients in the system. For example, the self-diffusion coefficient D is related to the time integral of the velocity correlation function ... 

By combining Eq. (44) and the recommended drag coefficient correlations in Table 8 or drag coefficient equations proposed by Turton and Levenspiel (1986), Eq. (34), and Haider and Levenspiel (1989), Eq. (35), the terminal velocity can be calculated. Haider and Levenspiel further suggested an approximate method for direct evaluation of the terminal velocity by defining a dimensionless particle size, d, and a dimensionless particle velocity, U, by... 

The entrainment velocity Ue is calculated fi-om the particle diameter according to Equation (3.70), the apparent coal density p, the gas density p, the gravitational acceleration g, and a drag coefficient Cd- The drag coefficient can be estimated by the correlation from Morsi et al. [135]... 

Krehenwinkel s work [23] includes empirical correlations for calculating the gas velocity at the flooding point, the pressure drop and the volumetric mass transfer coefficient in the gas and Uquid phases. 

It is known from experience with vertical pneumatic transport that the influence of weight prevails at low velocities, but as the velocity increases friction gains importance. Therefore, in the calculation of the pressure loss one must find not only the weight of the solids, which could be set up theoretically, but also an empirical relationship for vertical transport from the measured data. A correlation of the pressure-loss coefficient for vertical pneumatic conveyance according to data measured by Flatow " has been developed by Weber, and the result is... 

The heat transfer coefficient to the vessel wall can be estimated using the correlations for forced convection in conduits, such as equation 12.11. The fluid velocity and the path length can be calculated from the geometry of the jacket arrangement. The hydraulic mean diameter (equivalent diameter, de) of the channel or half-pipe should be used as the characteristic dimension in the Reynolds and Nusselt numbers see Section 12.8.1. 

At the conceptual stage for heat exchanger network synthesis, the calculation of heat transfer coefficient and pressure drop should depend as little as possible on the detailed geometry. Simple models will be developed in which heat transfer coefficient and pressure drop are both related to velocity1. It is thus possible to derive a correlation between the heat transfer coefficient, pressure drop and the surface area by using velocity as a bridge between the two1. 

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