Power Law Velocity Profile in Fully Developed Turbulent Pipe and Channel Flows

Abstract

The power law velocity profile has been analyzed in terms of the envelope of the friction factor which gives the friction factor log law. The power law index α and prefactor C are shown as the function of the friction Reynolds number, as well as the function of the alternate variable the nondimensional friction velocity. The fully developed turbulent superpipe flow data of McKeon et al. and fully developed channel flow data of Zanoun et al. have been analyzed and the power law index α and prefactor C data have been estimated, first as a function of the friction Reynolds number and second as function of the nondimensional friction velocity. Based on analysis, several correlations have been proposed that have been supported by the data.