An approximate boundary layer theory for semi-infinite cylinders of arbitrary cross-section

Abstract

An estimate is given of the distribution of skin frictional force per unit length, and of displacement area, on the outside of a semi-infinite cylinder, of arbitrary cross-section, moving steadily in a direction parallel to its generators. A Pohlhausen method is employed with a velocity distribution chosen to yield zero viscous retarding force on the boundary layer approximations. (The smallness of the fluid acceleration far from the leading edge has been pointed out by Batchelor (1954).) Like the Rayleigh method, this method is expected to yield reasonable results at large distances from the leading edge. However, for a large class of cross-sections, which includes all convex cross-sections and locally concave cross-sections with re-entrant angles greater than ½π, the method yields the expected square root growth of the boundary layer at the leading-edge, with a fairly close approximation to the coefficient, and it is supposed that the skin-frictional force and displacement area are given with reasonable accuracy along the whole length of the cylinder.

Results for the elliptic cylinder and the finite flat plate are given in closed form, valid for the whole length of the cylinder, and are expected to be in error by at most 20%. In addition, some estimate is given of the effect of corners on skin frictional force and displacement area.