Critical Reynolds Number
The critical Reynolds number is associated with the laminar-turbulent transition, in which a laminar flow becomes turbulent. This is an extraordinarily complicated process, which at present is not fully understood.
Critical Reynolds Number for Flow in a Pipe
For flow in a pipe of diameter D, experimental observations show that for “fully developed” flow, the critical Reynolds number is about Red,crit = 2300.
- Laminar flow. For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. The accepted transition Reynolds number for flow in a circular pipe is Red,crit = 2300.
- Transitional flow. At Reynolds numbers between about 2000 and 4000 the flow is unstable as a result of the onset of turbulence. These flows are sometimes referred to as transitional flows.
- Turbulent flow. If the Reynolds number is greater than 3500, the flow is turbulent.
Note that, the critical Reynolds number is different for every geometry.
Critical Reynolds Number in boundary layer flow over a flat plate.
Example: Critical Reynolds Number
A long thin flat plate is placed parallel to a 1 m/s stream of water at 20°C. Assume that kinematic viscosity of water at 20°C is equal to 1×10-6 m2/s.
At what distance x from the leading edge will be the transition from laminar to turbulent boundary layer (i.e. find Rex ~ 500,000).
In order to locate the transition from laminar to turbulent boundary layer, we have to find x at which Rex ~ 500,000.
x = 500 000 x 1×10-6 [m2/s] / 1 [m/s] = 0.5 m