A new explicit friction factor formula for laminar, transition and turbulent flows in smooth and rough pipes

Avci A., Karagoz İ.

EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, vol.78, pp.182-187, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 78
  • Publication Date: 2019
  • Doi Number: 10.1016/j.euromechflu.2019.07.007
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.182-187
  • Keywords: Friction factor, Pressure loss, Mathematical modeling, COLEBROOK-WHITE EQUATION, APPROXIMATIONS, LAW
  • Bursa Uludag University Affiliated: Yes


Pressure drop due to friction during internal pipe flow is one of the most important considerations in designing fluid and heat flow systems. There are many separate correlations valid for different situations such as laminar or turbulent rough and smooth surfaces for the estimation of friction factor. The present study introduces the derivation of a single explicit equation which is valid over the entire range of Reynolds number for both smooth and rough surfaces. This equation combines the laminar and turbulent friction factor equations through relation developed for the transition region. The results of the proposed equation were compared with the existing experimental data and the data from the Colebrook equation for smooth and rough surfaces respectively. The results show very good agreement with the experimental data as well as the Colebrook equation over the entire range of Reynold number. The percentage error lies within 2% and 10% for laminar and turbulent flows over the rough and smooth surfaces respectively. (C) 2019 Elsevier Masson SAS. All rights reserved.