### Abstract

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 × 10^{3} ≤ Re_{D} ≤ 35 × 10^{6}. 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 language | English (US) |
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Pages (from-to) | 429-443 |

Number of pages | 15 |

Journal | Journal of Fluid Mechanics |

Volume | 538 |

DOIs | |

State | Published - Sep 10 2005 |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Journal of Fluid Mechanics*,

*538*, 429-443. https://doi.org/10.1017/S0022112005005501