Let denote the mass concentration of species , which is the mass of species per unit volume of mixture. Given a total of concentration species, the local density of mixture is defined as

(19–1)

In a flow of a mixture, the chemical species are moving at different velocities. Let denote the velocity of species with respect to the coordinate system. The local mass-averaged velocity is given by

(19–2)

This is the local velocity that would be determined by means of a Pitot tube or other methods that measure force or pressure, and corresponds to v as commonly used for pure fluids. Other definitions of velocity, such as molar- and volume-averaged velocities, can also be used. They have, however, the inherent disadvantage that they do not appear explicitly in the fluid-mechanics equations [5].