where , and
subject to the boundary conditions and . Verify that
is a suitable solution of the previous differential equation, where .
Here, the symmetry axis of the jet is assumed to run along the -direction, whereas the -direction is perpendicular to this axis. The velocity of the jet parallel to the symmetry axis is
where , and as . We expect the momentum flux of the jet parallel to its symmetry axis,
to be independent of .
Consider a self-similar stream function of the form
Demonstrate that the boundary layer equation requires that , and that is only independent of when . Hence, deduce that and .
Demonstrate that satisfies
subject to the constraints that , and as . Show that
is a suitable solution, and that
where . Demonstrate that the displacement and momentum widths of the boundary layer are
Consider a boundary layer on a flat plate, for which . Show that, in the absence of suction,
but that in the presence of suction
Hence, deduce that, for a plate of length , suction is capable of significantly reducing the thickness of the boundary layer when