An Approximate Solution of the Laminar Boundary Layer on a Flat Plate with Uniform Suction

Extract

Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved.

Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.