Turbulent flow in smooth and rough pipes

Recent experiments at Princeton have revealed aspects of smooth pipe flow behavior that suggest a more complex scaling than previously noted. In particular, the results yield a new friction factor relationship for smooth pipes, and for the velocity profiles indicate the presence of a power law region near the wall and, for Reynolds numbers greater than 400 × 10³ (R⁺ > 9 × 10³), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with k_rms/D = 19.4 × 10^-6, over a Reynolds number range of 57 × 10³ to 21 × 10⁶, show that in the transitionally rough regime this surface follows an inflectional friction factor relationship rather than the monotonic relationship given in the Moody diagram. Outer scaling of the mean velocity data shows excellent collapse and strong evidence for Townsend's outer layer similarity hypothesis for rough walled flows. Finally, the pipe exhibited smooth behavior for k⁺_s ≤ 3.5, which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for Re_D ≤ 24 × 10⁶.