Hydrodynamic velocity

In Eq. (38) the hydrodynamic velocity is that used to evaluate the momentum of the phase. In viscous flow it is the term used in establishing the shear from a knowledge of the viscosity when effects of cross linking of fluxes (01, 02) are neglected. The hydrodynamic velocity and the diffusional velocity are related by... 

It should be recognized that the boundary conditions of the problem will establish the value of the hydrodynamic velocity, u. In the case of most turbulent flows the indirect influence of molecular diffusion on the hydro-dynamic velocity can be neglected. It should be emphasized that the hydrodynamic velocity is the time-average point velocity in Reynolds sense (R2). Under unsteady, nonuniform conditions of flow between parallel plates the material balance may be expressed for turbulent flow in the following form ... 

Equation (51) assumes that the eddy properties are isotropic. In addition, no effect of other gradients such as temperature or gravity upon the molecular transport is taken into account. The expression was written for a single component and it is necessary to solve a set of such expressions one for each component, simultaneously if the interrelation of the material transport upon the hydrodynamic velocity is to be taken into account. 

In cases where the electrode surfaces differ insignificantly and a one-to-one correspondence between them can be reached, the hydrodynamic velocity components normal to the electrode surfaces are negligibly small and the electrical field in the IEG is quasi-homogeneous (except for the near-electrode layers). In this case, the local, one-dimensional approximation method is used. 

Third, in the system of coordinates with the origin located at the surface of one of the electrodes, the hydrodynamic velocity field is two dimensional. Therefore, prescribing the distributions of hydrodynamic velocity, gas fraction, temperature, and so forth across the I EG, one can integrate the equations of mass, momentum, and energy transfer with respect to the distance between the electrodes. As a result, it is possible to reduce the problem s dimension by a unit. 

As a result, the fields of hydrodynamic velocity and pressure and the distributions of temperature and void fraction are determined. The current density is determined... 

In these equations D represents the general diffusion tensor for interacting particles, which may include hydrodynamic interactions. To simulate such Brownian motion, an efficient algorithm based on Eqs. 31 and 32 has been developed.149 This algorithm, written in its most general form, which accounts for interparticle (hydrodynamic) velocity-dependent interactions as well as direct interactions, is... 

The main distinction of the theory of a dynamic adsorption layer formed under weak and strong retardation arises when formulating the convective diffusion equation. At weak retardation the Hadamard-Rybczynski hydrodynamic velocity field is used while at strong retardation the Stokes velocity field. Different formulas for the dependence of the diffusion layer thickness on Peclet numbers are obtained. The problem of convective diffusion in the neighbourhood of a spherical particle with an immobile surface at small Reynolds numbers and condition (8.74) is solved, so that the well-known expression for the density distribution of the diffusion flow along the surface can be used. As a result, Eq. (8.10) takes the form (Dukhin, 1982),... 

As was covered earlier under deflagration and detona Vion, the detonation velocity of an explosive is the speed at which the detonation wave moves through the explosive. For most of today s (x>nimercial explosives, detonation velocity ranges from about 5,000 fps for ANFO to more than 22,000 fps for high explosives such as cast 50/50 Pentolite. It should also be noted that eveiy explosive compound v/ill have a maxxmuin or ideal detonation velocity, which is referred to as its hydrodynamic velocity. 

The response of the EQCM on rough surfaces cannot be treated in terms of the electrochemically defined roughness factor R, which is obtained from adsorption phenomena, e.g., from data such as presented in Fig. 22. This quantity can be considered as representing all adsorption sites on the surface, which is equivalent to the surface roughness on the atomic scale. However, the response of the EQCM depends on roughness on a mesoscopic scale, which is comparable to the hydrodynamic velocity decay length rather than to the double layer thickness. The width of the resonance is an important characteristic of the surface, as seen in Fig. 23b, and can serve as a semi-quantitative measure of its roughness on the scale relevant to the response of the EQCM. Unfortunately, only very few publications so far contain this information. 

The discussion of electrolyte solutions requires the estimation of the Reynolds number for the particular case where L is of the order of the mean diameter of the particles, i.e. 0.1 nm. All liquids commonly used as solvents show dynamic viscosities of the order of 1 cPoise and densities of the order of 1 g cm . Then the order of magnitude of Re can be evaluated if for U an estimate of the hydrodynamic velocity of the sphere in the liquid can be made. The order of magnitude of U can be derived from the linear transport theory, where the motion of a particle in a liquid is described at a local level by the action of a friction force F (eq 1.1). In the steady state of motion this force is supposed to equilibrate the thermodynamic force ... 

In what follows we sketch the steps of this theoretical formalism for nematics. The first class of hydrodynamic variables is associated with local conservation laws which express the fact that quantities like mass, momentum or energy cannot be locally destroyed or created and can only be transported. If p(r,t), g=pv(r,t) and e(r,t), where v is the hydrodynamic velocity, denote respectively, the density of these quantities, the corresponding conservation equations are ((Landau L.D. and Lifshitz E. 1964). 

Obtain the hydrodynamic velocities in the four sections of the column shown. The column cross-sectional area is Sc- The various volumetric flow rates entering or leaving the column are shown in Figure 7.P.I. 

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