Assume that the velocity profile in a boundary layer is replaced by a step profile, as
Chapter 9, Problem 9.52(choose chapter or problem)
Assume that the velocity profile in a boundary layer is replaced by a step profile, as shown in the figure, where the velocity is zero adjacent to the surface and equal to the free-stream velocity ( U) at a distance greater than 8. from the surface. Assume also that the density is uniform and equal to the free-stream density (p,,). The distance 8. (displacement thickness) is so chosen that the mass flux corresponding to the step profile is equal to the mass flux through the actual boundary layer. Derive an integral expression for the displacement thickness as a function of u, U,y, and 8.
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