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).

Sun Sep 28 22:13:11 EDT 1997