Discussion
Consider a flat plate, with a sharp leading edge, placed in a uniform flow of speed U. The direction of the free-stream flow is aligned with the plate. Assume that the flow is steady, incompressible and laminar. The thickness of the boundary layer at a fixed stream-wise location L from the leading edge of the plate is δ. Which one of the following correctly describes the variation of δ with U?
Answer: D
The boundary-layer thickness varies as δ \(\propto U^{-1/2}\).
For a laminar boundary layer on a flat plate, the Blasius solution gives
\[ \begin{aligned} \delta &\approx \frac{5.0\,x}{\sqrt{Re_{x}}} \\ &= 5.0\sqrt{\frac{\nu x}{U}} \end{aligned} \]
At a fixed location \(x = L\) and fixed viscosity, \(\delta\) is proportional to \(1/\sqrt{U}\): a faster stream gives a thinner boundary layer, because the momentum carried downstream outpaces the diffusion of viscous effects away from the wall.
The options with positive powers of \(U\) would make the layer thicken as the flow speeds up, the opposite of what happens. \(U^{1/2}\) is the right power with the wrong sign.
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