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Research Papers: Fundamental Issues and Canonical Flows

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

[+] Author and Article Information
Navid Azizi

Young Researchers and Elite Club,
Shiraz Branch, Islamic Azad University,
Shiraz 74731-71987, Iran
e-mail: zei.nav2006@gmail.com

Reza Homayoon, Mahmoud Reza Hojjati

Department of Chemical Engineering,
Shiraz Branch, Islamic Azad University,
Shiraz 74731-71987, Iran

1Corresponding 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 141(5), 051201 (Nov 08, 2018) (8 pages) Paper No: FE-18-1312; doi: 10.1115/1.4041232 History: Received May 02, 2018; Revised August 20, 2018

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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Figures

Grahic Jump Location
Fig. 1

Comparison between Colebrook–White f-data and those predicted by different correlations: (a) Brkić (Eq. (24)), (b) Sonnad and Goudar, (c) Samadianfard, (d) Ghanbari, (e) Brkić (Eq. (25)), (f) Haaland, (g) Chen, and (h) Romeo et al.

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Fig. 2

Predicted f-data by the new proposed correlation (Eq. (6)) versus Colebrook–White f-data

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Fig. 3

Predicted f-data by the new proposed correlation (Eq. (11)) versus Colebrook–White f-data

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Fig. 4

Calculated coefficient of determination for the studied correlations and the new equation

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Fig. 5

Calculated mean absolute error for the studied correlations and the new equation

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Fig. 6

Maximum values of absolute percent error of the two proposed approximations versus relative roughness (2000 ≤ Re ≤ 108)

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Fig. 7

Maximum values of absolute percent error of the two proposed approximations versus Reynolds number (10−6 ≤ (ε/D) ≤ 0.05)

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