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Boundary layers

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 tex2html_wrap_inline917 , 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 tex2html_wrap_inline923 , 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).

Vittorio Celli
Sun Sep 28 22:13:11 EDT 1997