- Fluid flows between two non-parallel plane walls, towards the intersection of the planes, in such a manner that
if
is measured along a wall from the intersection of the planes then
, where
is
a positive constant. Verify that a solution of the boundary layer equation (8.35) can be found
such that
is a function of
only. Demonstrate that this solution yields
- A jet of water issues from a straight narrow slit in a wall, and mixes with the surrounding water, which is at rest.
On the assumption that the motion is non-turbulent and two-dimensional, and that the approximations of boundary
layer theory apply, the stream function satisfies the boundary layer equation
Consider a self-similar stream function of the form

Suppose that

- The growth of a boundary layer can be inhibited by sucking some of the fluid through a porous wall.
Consider conventional boundary layer theory. As a consequence
of suction, the boundary condition on the normal velocity at the wall is modified to
, where
is the (constant) suction velocity. Demonstrate that, in the presence of suction, the von Kármán velocity
integral becomes

respectively. Hence, deduce thatConsider a boundary layer on a flat plate, for which . Show that, in the absence of suction,