One of the simplest flow configurations which illustrates the boundary layer
concept is the flow of a fluid parallel to a thin, flat plate; the geometry
is shown in Fig. 3.3. See also Tritton, page 102.
Figure 3.3: Geometry for viscous flow past a thin plate.
If the fluid were nonviscous, the streamlines would be
parallel to the plate and nothing very interesting happens. For a viscous
fluid, however, we must apply the no-slip boundary condition on the surface
of the plate. The thickness of the boundary layer, which will be denoted by 
, is the distance required for the velocity profile to approach its
free stream value. Recalling that the viscosity is a measure of the
diffusion of velocity (or vorticity), the thickness of the boundary layer
after a time t is approximately given by
Now in a time t an element of fluid which begins at the leading edge of
the plate will have moved a distance 
, so that the boundary layer
thickness a distance x from the leading edge is
Therefore, the boundary layer thickness at the trailing edge of the plate, measured relative to the length of the plate itself, is
where . We see that the boundary layer thickness decreases with increasing Reynolds number (for an assumed laminar flow).
