In order to make the idea of a boundary layer realistic, an arbitrary decision must be made as to its extent and the usual convention is that the boundary layer extends to a distance 6 from the surface such that the velocity и at that distance is 99% of the local mainstream velocity Ue that would exist at the surface in the absence of the boundary layer. Thus 6 is the physical thickness of the boundary layer so far as it needs to be considered and when defined specifically as above it is usually designated the 99%, or general, thickness. Further thickness definitions are given in Section 7.3.2.
7.2.1 Non-dimensional profile
In order to compare boundary-layer profiles of different thickness, it is convenient to express the profile shape non-dimensionally. This may be done by writing U = u/Ue and у = yjS so that the profile shape is given by u=f(y). Over the range у — 0 to у — 6, the velocity parameter й varies from 0 to 0.99. For convenience when using и values as integration limits, negligible error is introduced by using n = 1.0 at the outer boundary, and considerable arithmetical simplification is achieved. The velocity profile is then plotted as in Fig. 7.3b.