Turbulent Velocity Profile
Power-law velocity profile – Turbulent velocity profile
The velocity profile in turbulent flow is flatter in the central part of the pipe (i.e. in the turbulent core) than in laminar flow. The flow velocity drops rapidly extremely close to the walls. This is due to the diffusivity of the turbulent flow.
In case of turbulent pipe flow, there are many empirical velocity profiles. The simplest and the best known is the power-law velocity profile:
where the exponent n is a constant whose value depends on the Reynolds number. This dependency is empirical and it is shown at the picture. In short, the value n increases with increasing Reynolds number. The one-seventh power-law velocity profile approximates many industrial flows.