Turbulent flow in smooth and rough pipes

J. J. Allen, M. A. Shockling, G. J. Kunkel, A. J. Smits

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


Recent experiments at Princeton University have revealed aspects of smooth pipe flow behaviour that suggest a more complex scaling than previously noted. In particular, the pressure gradient results yield a new friction factor relationship for smooth pipes, and the velocity profiles indicate the presence of a power-law region near the wall and, for Reynolds numbers greater than about 400 × 103 (R+ > 9 × 103), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with krms/D= 19.4 × 10-6, over a Reynolds number range of 57 × 103-21 × 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-layer scaling of the mean velocity data and streamwise turbulence intensities for the rough pipe show excellent collapse and provide strong support for Townsend's outer-layer similarity hypothesis for rough-walled flows. The streamwise rough-wall spectra also agree well with the corresponding smooth-wall data. The pipe exhibited smooth behaviour for k s+ ≤ 3.5, which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for ReD≤24 × 106. The relationship between the velocity shift, ΔU//uτ, and the roughness Reynolds number, k s+, has been used to generalize the form of the transition from smooth to fully rough flow for an arbitrary relative roughness k rms/D. These predictions apply for honed pipes when the separation of pipe diameter to roughness height is large, and they differ significantly from the traditional Moody curves.

Original languageEnglish (US)
Pages (from-to)699-714
Number of pages16
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1852
StatePublished - Mar 15 2007

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


  • Pipe flow
  • Reynolds number
  • Roughness
  • Turbulence


Dive into the research topics of 'Turbulent flow in smooth and rough pipes'. Together they form a unique fingerprint.

Cite this