The character of flow within these two regions is entirely different. Considerable efforts have been made to determine the actual velocity profiles in pipe flows. Some of them are discussed here.

In viscous sub-layer, the velocity profile is written as,
                                          (11)
where is the distance measured from the wall, is the kinematics viscosity of the flow, is the time-averaged x -component of velocity and is called “friction velocity defined by,
                                          (12)
The "friction velocity" is not the actual fluid velocity rather it has same dimension as that of velocity. The Eq. (11) sometimes called as the ‘law of wall”. For smooth wall, Eq. (11) is valid very near to the wall for which .
In case of "overlap layer" the following expression commonly known as "Logarithmic Overlap Law" has been proposed;
                                        (13)