There are two important special cases of flows, namely laminar and turbulent flows, respectively. In the movie, the thin black lines of ink in the flowing water are in the laminar region of the fluid. Toward the bottom of the pipe (and later toward the right of the pipe) we see turbulent flow.

If the fluid flows slowly, the flow is usually laminar. If it flows fast, the flow is turbulent. A value of a combination of characteristic values of the flow—called the Reynolds number—tells us if a flow is laminar or turbulent.

The flow can be expressed in terms of the appropriate flow characteristic. For turbulent flow, the characteristic cannot be derived from first principles, in general. Normally it is measured.

laminar flow, laminar flow laws, turbulent flow laws, conductive flow

If the Reynolds number is smaller than a critical value (which depends upon the fluid and the pipe or duct or channel) the flow will be laminar. Above that there is a transition to turbulence.

There is no simple theory for turbulent flow. Engineers typically rely on experimental data to decide if a flow will be turbulent, and what characteristic to use in that case.

Turbulente Strömung