Discussion
An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be
Answer: C
The boundary layer becomes 0.5 mm thick.
At a Reynolds number of 1000 the flow is laminar, and the Blasius result for a flat plate is:
\[ \delta = \frac{5x}{\sqrt{Re_{x}}} \propto \frac{1}{\sqrt{U}} \]
At the same location, x is fixed, so increasing the velocity four times divides the thickness by \(\sqrt{4}=2\): 1 mm becomes 0.5 mm.
0.25 mm assumes thickness inversely proportional to velocity, and 2 or 4 mm have the thickness growing with velocity, the wrong direction. A faster stream thins the boundary layer.
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