The Boundary Layer and Skin Friction for a Figure of Revolution

Abstract The boundary-layer equations for a figure of revolution are first derived in the Prandtl form. These are then integrated to give the so-called “integral relation” for the case in question. Power-series expressions for the boundary-layer profiles in laminar and turbulent flow are assumed and substituted into the integral relation. In this way expressions are obtained for the boundary-layer thickness and for the contribution to the skin friction of the laminar and turbulent portions of the boundary layer. In particular a simple expression is given for the boundary-layer thickness at the stagnation point, which is a singular point of the equation. Conditions at the point where the boundary-layer flow changes from laminar to turbulent are discussed in some detail, and the simple Prandtl assumption for the transition-point behavior is adopted as the basis of the further calculations. Numerical values for the N.P.L. International Airship Model are introduced, and theoretical curves are given for the resistance coefficient as a function of the Reynolds number. These are compared with previous theoretical results and with experimental values. The agreement of the theory with experiment is considered satisfactory in view of the assumptions which had to be introduced into the analysis in order to supplement the present state of knowledge concerning boundary-layer phenomena. The general integral relation developed in the paper can be used to obtain more accurate results in the future, when more is known regarding boundary-layer profiles in curved and diverging (or converging) flows.