The boundary layer produces a drag on the plate due to the viscous stresses which are developed at the wall. The viscous stress at the surface of the plate is

Once this stress is known, we have only to integrate it over the surface of
the plate to obtain the total drag force *D*:

To get an estimate of the velocity gradient near the wall, we note that by definition the width of the boundary layer is the distance over which the velocity returns to its free stream value, so

Performing the integral to obtain the drag, we find

Defining the coefficient of drag for the plate as
*C _{D} = D/*(r

not far from our simple estimate. This drag is often referred to as *skin friction* , and is due to the viscous stresses acting on the
surface of the plate. If the boundary layer remains attached to the body
(which it may not; see below), then this is the sole source of aerodynamic
drag on a body. At high Reynolds numbers, say , this gives a drag
coefficient of , which is relatively small.

The previous analysis assumed that the flow in the boundary layer was
laminar. However, in large Reynolds number flow we often encounter *turbulent boundary layers* , which tend to produce a larger drag. The
turbulent mixing of the fluid near the surface of a solid body leads to more
efficient momentum transport away from the body, increasing the gradient of
the velocity profile at the surface and therefore the viscous stress on the
plate. For boundary layers which remain attached to a body the drag due to
skin friction can be reduced if the boundary layer can be persuaded to remain
laminar.

Sun Sep 28 22:13:11 EDT 1997