Discussion
For the laminar, incompressible flow over a flat plate with uniform free stream velocity, the axial pressure gradient within the boundary layer is
Answer: C
The axial pressure gradient is equal to zero.
Outside the boundary layer the free stream is uniform, so by Bernoulli's equation \(dp/dx = -\rho U\,dU/dx = 0\). Boundary-layer theory shows that the pressure does not vary across the thin layer (\(\partial p/\partial y \approx 0\)), so the layer feels the same zero gradient. This is the Blasius flat-plate problem.
A positive (adverse) or negative (favourable) gradient arises only when the outer velocity changes along the surface, as over a curved body. Pressure gradient and velocity gradient have different dimensions, so they cannot simply be equal.
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