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Although the viscosity of a fluid such as air or water is so small that, over most of the flow, the viscous stresses are utterly negligible in comparison with the inertial forces acting on a fluid element, there must nevertheless exist, immediately adjacent to any solid surface, a thin region in which the velocity rises steeply from zero at the wall, where the fluid adheres to the surface, to the value it would have had if the fluid had been entirely free of friction.

It is precisely because this region is so thin that the velocity gradient across it becomes large enough for the viscous term, which is the product of a very small coefficient and a very large gradient, to remain comparable in magnitude to the inertial terms, and it is this balance, rather than any smallness of the viscosity itself, that determines how the thickness of the layer grows with distance along the surface.

Consequently, the classical procedure of first solving the inviscid problem for the outer flow and then correcting it near the wall is not merely a computational convenience but a reflection of the physical fact that the two regions are governed by different dominant balances.