Boundary Layer over a Thin Needle

Abstract

An equation governing the motion of an incompressible fluid flowing axially over a thin paraboloid of revolution is derived. The asymptotic behaviors and an approximate solution are discussed, and numerical solutions computed. From the numerical solutions, an extrapolation towards vanishing boundary thickness is made. It is found that for progressively thin needles, the displacement thickness and drag per unit length diminish very slowly, but eventually become zero as the needle vanishes.