An Equation for the Mean Velocity Distribution of Boundary Layers

A general relation, empirical in origin, for the mean velocity distribution of both laminar and turbulent boundary layers is proposed. The equation, in general, accurately describes the profiles in both laminar and turbulent flows. The calculation of profiles is based on a prior knowledge of momentum, displacement, and boundary-layer thickness together with free-stream conditions. The form for turbulent layers agrees with the present concepts of similarity of the outer layer. For the inner region or turbulent boundary layers the present relation agrees very closely with experimental measurements even in cases where the logarithmic law of the wall is inadequate. A unique relation between profile form factors and the ratio of displacement thickness to boundary-layer thickness is obtained for turbulent separation. A similar criterion is also obtained for laminar separation. These relations are demonstrated to serve as an accurate criterion for identifying separation in known profiles.