Scaling of the Mean Velocity Profile for Turbulent Pipe Flow

Abstract

An experimental investigation was conducted to determine the scaling of the mean velocity profile for a fully developed, smooth pipe flow. Measurements of the mean velocity profiles and static pressure gradients were performed at 26 different Reynolds numbers between $31\ifmmode\times\else\texttimes\fi{}{10}^{3}$ and $35\ifmmode\times\else\texttimes\fi{}{10}^{6}$. The profiles indicate two overlap regions: one which scales as a power law and one which scales as a log law, where the log law is only evident when the Reynolds number exceeds approximately $300\ifmmode\times\else\texttimes\fi{}{10}^{3}$. It is proposed that the velocity scales for the inner and outer regions are different, which is contrary to commonly accepted beliefs.