Various studies have shown that the critical Reynolds number
for a flow between a Darcy and a non-Darcy flow is 10, and that for different porous media, this limit is slightly different [31, 32].
In particular, a major unsolved problem is to theoretically obtain the minimum critical Reynolds number
[R.sub.c,min] [approximately equal to] 2050, which was first observed by Osborne Reynolds in 1883 .
With the use of (10) and 11) the critical Reynolds number
can be estimated as follows:
Whether the fluid moving as laminar or turbulent flow can be decided by the value of Reynolds number, there is a lower bound around 2000 for the critical Reynolds number
, which transits laminar flow to turbulence.
The key point is that the flow around a smooth sphere the size of a golf ball travelling through stationary air at the speeds experienced when driven from the tee is nominally laminar and just below the critical Reynolds number
. The effect of dimpling the surface of the ball is to energise the flow and trigger turbulence.
While a general critical Reynolds number
cannot characterize the transition between the two regimes, it is possible, as will be shown, for a single suitably scaled Reynolds number to provide a reasonable approximation of the transition region.
The critical Reynolds number
shows a non-monotonous variation with the degree of blockage, [beta].
 state that previous experiments have revealed a value for a critical Reynolds number
and boundary layer thickness.
Ghajar and Madon (1992) performed an extensive study into the effect of three different types of inlets on the critical Reynolds number
during isothermal, fully developed flow.
Harms et al.6 found that for deep rectangular micro-channels having an aspect ratio of 0.244 the critical Reynolds number
is about 1500.
Note that the critical Reynolds number
for fully developed oscillations in this paper is 250.
Or it would vibrate until you got to a critical Reynolds number
, and then it would stop and wouldn't vibrate again."