Universal Logarithmic Law of the Wall in Turbulent Channel and Pipe Flows

The accuracy of obtaining parameters of velocity distribution in the inertial sub-layer of wall-bounded flows depends on evaluating the wall friction and spatial resolution of measurements. By focusing on these aspects of experiments and extending the range of available channel data by a factor of two, our work confirms the log-law over a power-law representation for Reτ ≥ 2 × 10. Measurements in a fullydeveloped pipe reveal that velocity instruments such as hot-wires are superior to pressure probes for several reasons including spatial resolution. No general technique for correcting Pitot probe data exists, and the MacMillan’s displacement correction drastically changes the slope of the logarithmic law. Oil-film interferometry coupled with hot-wire measurements were used to demonstrate effects of channel aspect ratio on results and to reveal that initial tripping has insignificant effects on the Karman constant in the fully developed region. Data reveal evidence on differences in the outer flow between channels and pipes. In channels, we find that the inertial sub-range may be represented by the simple approximate formula U ≈ e ln y + 10/e and the fully developed channel resistance by cf = 0.0624Re−0.25 m or √ 2/cf ≈ e lnRem √ cf + 10/e+ e (ln 1/ √ 2− 1) where Rem = Uh/ν, h being the channel half hight.