## Abstract

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 × 10^{3} (R^{+} > 9 × 10^{3}), 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 × 10^{3}-21 × 10^{6}, 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 Re_{D}≤24 × 10^{6}. The relationship between the velocity shift, ΔU//u_{τ}, 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 language | English (US) |
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Pages (from-to) | 699-714 |

Number of pages | 16 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 365 |

Issue number | 1852 |

DOIs | |

State | Published - Mar 15 2007 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

## Keywords

- Pipe flow
- Reynolds number
- Roughness
- Turbulence