Discussion
Consider a steady, and incompressible flow over a body with characteristic length L. The boundary layer thickness at a distance x from the leading edge is \(\delta\). Which one of the following assumptions is correct for deriving the Prandtl boundary layer equations?
Answer: D
The assumption is \(\delta \ll L\).
Prandtl's boundary layer equations come from an order-of-magnitude analysis of the Navier-Stokes equations in a thin layer next to the wall. Because the layer is thin compared with the body length, gradients across it (in y) are much larger than gradients along it (in x). This lets the streamwise diffusion term \(\partial^{2}u/\partial x^{2}\) be dropped and shows that the pressure is nearly constant across the layer, imposed by the outer flow.
If \(\delta\) were comparable to or larger than L, none of these simplifications would hold, which rules out the other three options.
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