, with *u* being the “typical“ velocity, *L* being the „typical“ long measure and | | being the |

kinematical viscosity. The characteristic length L is used for the description of fluid-transport processes (hydrodynamics, mass transport, heat transport, etc.) in so-called dimensionless index numbers, such as the Reynolds-number or Prandtl-number. It has the dimension of a length, but describes the three-dimensional geometry of a reference system. In simplified terms we apply for the characteristic length in the Reynolds number the diameter if there is a pipe flow or the water depth if we have an open channel flow.

The critical Reynolds number for pipe flow is about 580, so that for example the flow within a pipe with the diameter D=0,20 m is turbulent if the flow velocity is greater than ~ 3 mm/s. This observation makes clear that most of the flows with technical relevance are turbulent. One of the few exceptions is for example human blood vessels that have laminar flow as a general rule (…maybe except for the aorta).