The axisymmetric boundary layer on a long thin cylinder

Abstract

The laminar boundary layer in axial flow about a long thin cylinder is investigated by two methods. One (§2) is a Pohlhausen method, based on a velocity profile chosen to represent conditions near the surface as accurately as possible. The other (§3) is an asymptotic series solution, valid far enough downstream from the nose for the boundary-layer thickness to have become large compared with the cylinder radius. Another series solution (due to Seban, Bond and Kelly) is known, valid near enough to the nose for the boundary layer to be thin compared with the cylinder radius. The Pohlhausen solution shows good agreement with both series, near and far from the nose, and enables an interpolation to be made (§4) between them in the extensive range of distances from the nose for which neither is applicable. The final recommended curves, for the variation along the cylinder of skin friction, boundary-layer displacement area and momentum defect area, are displayed in graphical and tabular form (figure 1 and table 1) and are expected to be correct to within about 2%. The velocity near the wall is closely proportional to the logarithm of the distance from the axis; this is the profile used in the Pohlhausen method. The analogy with the distribution of mean velocity in turbulent flow over a flat plate is discussed at the end of §2.