# Is theoretically possible to have the laminar flow above $Re=10^7$?

The onset of turbulent flow ranges greatly, for pipe flow I came across the information that the onset of turbulent flow occurs at approximately $$Re=10^4$$, while for boundary layers on the airplane's wing the onset can be as high as $$Re=10^6$$ to $$Re=5\cdot 10^6$$. Therefore, is theoretically possible to have the laminar flow above $$Re=10^7$$, disregarding the laminar sublayer (that occurs in flow over the surfaces) in every turbulent flow? Any reference to books would be highly appreciated.

Sure, it's possible. These guidelines are just that -- guidelines -- and it's possible that different flow configurations would be outside of those guides.

For example, the flow over a wing guideline is based on a wing at normal conditions, flying freely in the atmosphere in straight and level flight. But if that wing were in a converging duct, where there is a strong, favorable pressure gradient, then the transition may be delayed to much higher Reynolds numbers.

Another example is a wing that has boundary layer suction devices. These work by sucking in air through the surface of the wing and also delay transition to turbulence well beyond the usual range.

Lastly, and this is a bit of a cheating way to do it, but remember how Reynolds number is defined -- we pick the length scale and the velocity that we think is relevant. So if we're talking about an airplane flying and we pick the length of the fuselage to define the Reynolds number instead of the chord of the wing, then our Reynolds numbers could be an order of magnitude larger just because we defined them that way.

So in the end, all of those rules of thumb about when stuff happens with Reynolds number are just correlations over a huge number of different experiments/simulations/conditions. There are always going to be outliers, but on average, these things hold true and that makes them useful for engineering and design.