The present paper describes the results of a stability investigation on symmetrical velocity profiles in a channel and of boundary-layer profiles. The effect of friction was assumed to be vanishing and did not occur in the stability consideration so far as it had been resorted to for preparatory asymptotic considerations. Proceeding on very general premises as regards the form of the velocity distribution, a proof was deduced of the elementary theorem that velocity profiles with inflection points are unstable.

The system of linear differential equations which indicated the approach of separation and the so-called "boundary-layer thickness" by Gruschwitz is extended in this report to include the case where the friction layer is subject to centrifugal forces. Evaluation of the data yields a strong functional dependence of the momentum change and wall drag on the boundary-layer thickness radius of curvature ratio for the wall. It is further shown that the transition from laminar to turbulent flow occurs at somewhat higher Reynolds Numbers at the convex wall than at the flat plate, due to the stabilizing effect of the centrifugal forces.

The tendency toward economy of material and lightness of structure has long since led to the increased application of beams having large ratios of moment of area W to cross-sectional area F. This paper tries to provide an answer to how thin the beams can be.