A new friction factor relationship for fully developed pipe flow

B. J. McKeon, M. V. Zagarola, A. J. Smits

Research output: Contribution to journalArticlepeer-review

157 Scopus citations


The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range 31 × 103 ≤ ReD ≤ 35 × 106. The constants of Prandtl's 'universal' friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5 %, and yield a value for the von Kármán constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4 % and agrees with the Blasius relationship for low Reynolds numbers to within 2.0 %.

Original languageEnglish (US)
Pages (from-to)429-443
Number of pages15
JournalJournal of Fluid Mechanics
StatePublished - Sep 10 2005

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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