United Formula for the Friction Factor in the Turbulent Region of Pipe Flow

Friction factor is an important element in both flow simulations and river engineering. In hydraulics, studies on the friction factor in turbulent regions have been based on the concept of three flow regimes, namely, the fully smooth regime, the fully rough regime, and the transitional regime, since the establishment of the Nikuradze’s chart. However, this study further demonstrates that combining the friction factor with Reynolds number yields a united formula that can scale the entire turbulent region. This formula is derived by investigating the correlation between friction in turbulent pipe flow and its influencing factors, i.e., Reynolds number and relative roughness. In the present study, the formulae of Blasius and Stricklerare modified to rearrange the implicit model of Tao. In addition, we derive a united explicit formula that can compute the friction factor in the entire turbulent regimes based on the asymptotic behavior of the improved Tao’s model. Compared with the reported formulae of Nikuradze, the present formula exhibits higher computational accuracy for the original pipe experiment data of Nikuradze.

• Publication year

  2016

• Venue

  PLoS ONE

• Publication date

  2016-05-02

• Fields of study

  Mathematics, Medicine, Engineering, Environmental Science

• Identifiers
  DOI 10.1371/journal.pone.0154408PMID 27136099PMCID 4852912
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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