The most often used correlation is the "empirical power law velocity profile" defined by,
                                        (14)
where is the centerline velocity and holds good for many practical flow problems.

Moody Chart

The fundamental difference between laminar and turbulent flow is that the shear stress for laminar flow depends on the viscosity of the fluid whereas in case of turbulent flow, it is the function of density of the fluid. In general, the pressure drop , for steady, incompressible turbulent flow in a horizontal round pipe of diameter can be written in the functional form as,
                                        (15)

where is the average velocity, is the length of the pipe and is a measure of the roughness of the pipe wall. Similar expression can also be written for the case of laminar flow in which the term will be absent because the pressure drop in laminar flow is found to be independent of pipe roughness i.e.
                                        (16)