x – momentum equation
The Navier-Stokes equations in x-direction in conservative form (using continuity equation) is given as
Figure 27.3: Control volume for x-momentum equation
Intergrading over the - control volume (Figure 27.3)
Application of the Green's theorem to the x-momentum equation (see Fig. 27.3) leads to
where and are defined as
and
and are axial and transverse fluxes of x-momentum.
Thus
The linearized forms of these equations are
- control volume (Figure 27.3) 
and 
are defined as 
and 
are axial and transverse fluxes of x-momentum. 
