layers as equivalent to exterior unbounded boundary layers. δmax thickness The location of the velocity peak, denoted as is an obvious demarcation location for the unbounded boundary layer. The main appeal of this choice is that this location is approximately the dividing location between the viscous and inertial regions. For the laminar flow simulation along a wing, umax located at δmax is found to approximate the viscous boundary layer thickness given as + indicating the velocity peaks just above the viscous boundary layer thickness δv. For the inertial regions of both laminar and turbulent flows, is a convenient lower boundary for the moment integrals. If the width, , is calculated using as the mean location then the boundary layer thickness, defined as the point where the velocity essentially becomes u0 above the wall, can then be properly identified. The 99% boundary layer thickness A significant implication of the peaking behavior is that the 99% thickness, , is NOT recommended as a thickness parameter for the exterior flow, unbounded boundary layer since it no longer corresponds to a boundary layer location of consequence. It is only useful for unbounded laminar flow along a very thin flat plate at zero incidence angle to the flow direction since the peak for this case will be very small and the velocity profile will be closely approximated as the bounded boundary layer case. For thick plates-walls, non-zero incidence angles, or flow around most solid surfaces, the excess flow due to form drag results in a near-wall peak in the velocity profile making not useful. Displacement thickness, momentum thickness, and shape factor The displacement thickness, momentum thickness, and shape factor can, in principle, all be calculated using the same approach described above for the bounded boundary layer case. However, the peaked nature of the unbounded boundary layer means the inertial section of the displacement thickness and momentum thickness will tend to cancel the near wall portion. Hence, the displacement thickness and momentum thickness will behave differently for the bounded and unbounded cases. One option to make the unbounded displacement thickness and momentum thickness approximately behave as the bounded case is to use umax as the scaling parameter and δmax as the upper integral limit. Further reading Rosenhead, Louis, ed. Laminar boundary layers. Clarendon Press, 1963. Lagerstrom, Paco Axel. Laminar flow theory. Princeton University Press, 1996. Schlichting, Hermann, Boundary-Layer Theory, 7th ed., New York: McGraw-hill, 1979. Frank