The momentum equation for the fluid considers the effects of convection, pressure force, viscous stress, and turbulent transport, as well as the impact from liquid sprays and body force:

(2–3)

where p is the pressure, is the rate of momentum gain per unit volume due to the spray, g is the specific body force, is the viscous shear stress given by

(2–4)

in which is the laminar kinematic viscosity, I is the identity tensor, and superscript T means transpose of a tensor. The stress 𝚪 accounts for the effects of ensemble-averaging or filtering of the nonlinear convection term, that is, . In the RANS approach, it is called the Reynolds stress; in the LES approach, it is called the SGS stress. In both cases, turbulence models are needed to provide closure.