In internal flow, when a fluid flows inside a circular pipe, the most practical value of critical Reynolds number is taken as 2300. I was wondering if this number is also the same for non circular ducts? Does the critical Reynolds number of a duct will also be around 2300 for most practical cases?

  • $\begingroup$ The transition range is normally taken as 1700 to 2300 but laminar flow has been found outside these values under controlled conditions. $\endgroup$
    – Solar Mike
    Aug 7, 2021 at 14:11
  • $\begingroup$ There are relatively simple scaling laws for arbitrary polygon shapes. Here's a paper: researchgate.net/publication/… $\endgroup$
    – Pete W
    Aug 7, 2021 at 15:34

1 Answer 1


To my understanding, if a flow has a different geometry, such as flow in a square duct, or over a turbine blade, transition will occur at different values of Re.

Additionally another very important point is that in circular tube:

  • if the flow is undisturbed (i.e. very smooth pipe walls) then the transition to transient flow is at much greater Re numbers
  • if Re is less than 2000, then the flow will always be laminar even when it is disturbed.
  • $\begingroup$ That was useful. $\endgroup$ Aug 7, 2021 at 12:53

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