Conservation of momentum in an inertial (non-accelerating) reference frame is described by [47]

(1–3)

where is the static pressure, is the stress tensor (described below), and and are the gravitational body force and external body forces (for example, that arise from interaction with the dispersed phase), respectively. also contains other model-dependent source terms such as porous-media and user-defined sources.

The stress tensor is given by

(1–4)

where is the molecular viscosity, is the unit tensor, and the second term on the right hand side is the effect of volume dilation.

For 2D axisymmetric geometries, the axial and radial momentum conservation equations are given by

(1–5)

and

(1–6)

where

(1–7)

and is the swirl velocity. (See Swirling and Rotating Flows for information about modeling axisymmetric swirl.)