Scaling Laws for Fully Developed Turbulent Flow in Pipes

Abstract

Mathematical and experimental evidence is presented to the effect that the velocity profile in the intermediate region of turbulent shear flow in a pipe obeys a Reynolds-number dependent scaling (power) law rather than the widely believed von Kármán-Prandtl universal logarithmic law. In particular, it is shown that similarity theory and the Izakson-Millikan-von Mises overlap argument support the scaling law at least as much as they support the logarithmic law, while the experimental evidence overwhelmingly supports the scaling law. This review article includes 39 references.