Determination of friction factor (f) in pipe flow is necessary for various applications dealing with fluid flow. The Colebrook–White equation is the most accepted technique for the f-values estimation in turbulent flow. The biggest problem with this equation is that it can only be solved using numerical iteration methods. This paper contributes two new formulas based on the Colebrook–White equation to calculate f for the turbulent flow regime. To determine the new correlations, several equations were first suggested and then their coefficients were determined using the curve fitting method. Thereafter, based on various statistical error calculations, two equations with the highest accuracies were selected for the further modification. The advantages of the proposed correlations are that they are explicit in f so they do not need any iteration to compute friction factor and the results of calculating f-values reveal that the two new equations are of maximum absolute percent errors (APE) of 0.91% and 3.49% over the entire applicability range of Colebrook–White equation.

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# Predicting the Colebrook–White Friction Factor in the Pipe Flow by New Explicit Correlations

Navid Azizi

,
Navid Azizi

Young Researchers and Elite Club,

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

e-mail: zei.nav2006@gmail.com

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

e-mail: zei.nav2006@gmail.com

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Reza Homayoon

,
Reza Homayoon

Department of Chemical Engineering,

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

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Mahmoud Reza Hojjati

Mahmoud Reza Hojjati

Department of Chemical Engineering,

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Search for other works by this author on:

Navid Azizi

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

e-mail: zei.nav2006@gmail.com

Reza Homayoon

Department of Chemical Engineering,

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Mahmoud Reza Hojjati

Department of Chemical Engineering,

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

Shiraz Branch, Islamic Azad University,

Shiraz 74731-71987, Iran

1

Corresponding author.
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 2, 2018; final manuscript received August 20, 2018; published online November 8, 2018. Assoc. Editor: Shawn Aram.

*J. Fluids Eng*. May 2019, 141(5): 051201 (8 pages)

**Published Online:**November 8, 2018

Article history

Received:

May 2, 2018

Revised:

August 20, 2018

Citation

Azizi, N., Homayoon, R., and Hojjati, M. R. (November 8, 2018). "Predicting the Colebrook–White Friction Factor in the Pipe Flow by New Explicit Correlations." ASME. *J. Fluids Eng*. May 2019; 141(5): 051201. https://doi.org/10.1115/1.4041232

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