Fluid momentum boundary conditions on rigid walls are introduced either by imposing a value of the velocity at the wall wall, or by calculating shear stress at the wall and modifying the local flow velocity accordingly.
On no-slip walls, the gas velocity is set equal to the wall velocity:
 | (3–2) |
In this case, the wall shear stress is then determined implicitly through Equation 2–3.
On free-slip and turbulent law-of-the-wall boundaries the normal gas velocity is set equal to the normal wall velocity,
 | (3–3) |
and the two tangential components of the wall shear stress are explicitly specified. For free-slip walls the tangential components of the wall shear stress are zero. For turbulent flow conditions the tangential shear stress can be determined by the "law of the wall":
 | (3–4) |
Where 
is the shear speed or friction velocity, which is related to the
wall shear stress 
by
 | (3–5) |
The tangential velocity 
is defined as 
. The Reynolds number based on the gas velocity relative to the
wall is 
, which is evaluated a distance y from the
wall, taken to be the wall-adjacent cell size. The Reynolds number 
defines the transition from the logarithmic regime (when
) to the viscous sublayer regime (
). In the viscous sublayer regime, the laminar formula for shear
stress is used. In the logarithmic regime's formulation, the wall unit
(
) is replaced with the following approximation to decouple the
solution for 
[4]:
 | (3–6) |
In Equation 3–4, Equation 3–5, and Equation 3–6 it is assumed that
the wall-adjacent cell size y is small enough to be in the
logarithmic regime or the laminar sublayer of the turbulent boundary layer. The
constants κ, 
, 
, and B in Equation 3–4 are related to
the k-ε model constants. Commonly used values are found
in the KIVA-II documentation [4]. With the shear stress
(
) calculated from Equation 3–4 and Equation 3–5, the total change
in fluid momentum occurring in a time step due to wall friction can be calculated in
the cell. This change is apportioned to the vertices in the cell that are on the
wall surface, and are effected for the momentum of those vertices [4].
It is noted that the logarithmic formulation used in Equation 3–4 assumes a smooth wall. If wall roughness must be considered, the following equation is used:
 | (3–7) |
in which roughness effects 
is modeled as [14], [6],
 | (3–8) |
and 
, where 
is the roughness height. 
is a constant depending on the type of surface roughness.