Volumetric fluxes, average

A general expression for average void fraction in an adiabatic two-phase flow or in saturated boiling was suggested by Zuber and Findlay (1965). Defining the local superficial velocities, VSG(= Qc/A) and VSL (= QJA), as volumetric flux densities, they assumed the velocity and void distributions to be... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

In all ultrafiltration systems reported in the literature, average volumetric flux rates at consecutively increasing lengths along the conduit are not measured. As a result it is not possi-... 

Finally the Sq parameter can for instance, be related to as proposed by Darton and Harrison [21]. To this end, the concept of drift fl ix, volumetric flux of gas relative to a surface moving at the average velocity, is used. It is considered... 

To render eqn (13.1) dimensionless, it is first necessary to select convenient reference levels for all the variables x, y, z, t, and p. The choice is quite arbitrary. For the distance variables (x, y and z) the reference level L would typically consist of a key equipment dimension - a tube or tank diameter, or the length of a submerged object, etc. for velocity an average value or an entering volumetric flux V and for the remaining variables t and p) appropriate combinations of the other reference level can be constructed for example, LjV for t, and pfV for p. 

Here, /p is the filtrate flux (cm min ) averaged over the hollow fiber membrane of length L (cm) and is the shear rate (s ) on the membrane surface, as in Equation 8.6. The volumetric percentage of red blood cells (the hematocrit) was taken as C, and its value on the membrane surface, Cg, was assumed to be 95%. 

Single-phase flow means that only one fluid phase is present in the void space (implying, most importantly, that no fluid-fluid interface exists). The superficial velocity i is a volume flux based on the total cross section of the material. (For flow in a packed colunm, V = Q/A, where Q is the volumetric flow rate and A is the column cross-sectional area.) The interstitial velocity, Vint = v/e, better characterizes the average fluid velocity actually present in the voids. 

MOLAL FLOW RATE, VELOCITY, AND FLUX. If the total molal flux, in moles per unit time per unit area in a direction perpendicular to a stationary plane, is denoted by N and the volumetric average velocity by mq,... 

Difliisivities are defined, not with respect to a stationary plane, but relative to a plane moving at the volume-average velocity Mq. By definition there is no net volumetric flow across this reference plane, although in some cases there is a net molar flow or a net mass flow. The molar flux of component A through this reference plane is a diffusion flux designated and is equal to the flux of A for a stationary plane [Eq. (21.2)] minus the flux due to the total flow at velocity Mq and concentration... 

The component balance equation is expressed with mass fractions of the individual species, cOt and the density of the reaction mixture, Pg. In Eq. (5.1) Ft is the total volumetric flow rate, = zjL the dimensionless reactor length. The first term on the right-hand side corresponds to sources by chemical reactions the second term quantifies the local mass fluxes, jj(< ), entering through the membrane. In the FBR model the flux term is omitted. The catalyst density is denoted by p t and e is the averaged porosity of the catalyst bed. Vr is the reactor volume. Mi the molecular mass of species i, the surface area of the membrane wall. The reaction rate rj represents the jth rate of the overall Nr reactions taking place. 

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