Page 170 - Industrial Ventilation Design Guidebook

i 3 2 CHAPTER 4 PHYSICAL FUNDAMENTALS

The total mass balance is the sum of Eqs. (4.260) and (4.261):

where p = p A + p B . For a two-component or binary mixture, M Ar A + M Br B = 0
is valid.
The mass flow density of the mixture in the x direction is defined by

with corresponding equations for other directions or velocities u y and u v Us-
ing these notations, the mass balance of the mixture (Eq. (4.262)) is written as

For the mass balance of component A, diffusion velocity and the corre-
sponding diffusion factor are defined with regard to the mean molar velocity
v, defined by the equation

where v Ax is the velocity of component A in the x direction, assuming a stable
coordinate system. According to this the mass flow density is

The velocity of the mass center of the system, u x (Eq. (4.263)), can be written as

using velocities v Ax and v Bx. The mass flow density may be written in the fol-
lowing ways:

In a boundary layer equation the mass center is considered with the help
of the velocity (u x, u^ u z) and therefore a distribution of the velocity of the
mass center is desirable. The diffusion velocity and diffusion factor are deter-
mined with regard to velocity v x, giving a formula for v Ax - v,., but not for
V U
AX~ X • A useful approach is offered by Eq. (4.268c), using the artificial
multiplication factor (v^ - u x)/(\ Ax - v.,,).
From Eq. (4.267) and p = p A + p s, it is seen that the following equation is
valid: