New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

Fang, Xiande; Xu, Yu; Zhou, Zhanru

doi:10.1016/j.nucengdes.2010.12.019

Cited by 242 publications

(108 citation statements)

References 25 publications

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“…Relative error (RErr) was determined using equation (10) [36] and Ghanbari et al [52]. This result shows that Microsoft Excel Solver can be used to develop Fff for estimating the Ff.…”

Section: Methodsmentioning

confidence: 98%

“…Despite more than seven decades of research, a lower error and full understanding of the essentials of this phenomenon is still far from complete. [32] Brkic [33,34] , Danish et al [35] , Fang et al [36] , Mustafa et al [37] performance evaluation of each of these Fff with particular attention to accuracy using statistical techniques with a larger aim of providing error free formula for Ff computation.…”

Section: Introductionmentioning

confidence: 99%

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Accurate solutions of Colebrook-White’s friction factor formulae

Lukman¹,

Oke²

2018

Nig. J. Tech.

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Estimations of friction factor (Ff) in pipeline systems and fluid transport are essential ingredients in engineering fields and processes. In this paper explicit friction factor formulae (Fff) were proposed and evaluated with an aim of developing error free Fff. General Fff that relate Ff, Reynolds number (Re) and relative roughness (Rr) were proposed. Colebrook -White's formula was used to compute different Ff for Re between 4 x 10 3 and 1.704 x 10 8 , and Rr between 1.0 x 10 -7 and 0.052 using Microsoft Excel Solver to fix the Fff. The fixed Fff were used to compute Ff for Re between 4 x 10 3 and 1.704 x 10 8 and Rr between 1.0 x 10 -7 and 0.052. Accuracy of the fixed Fff was evaluated using relative error; model of selection (MSC) and Akaike Information Criterion (AIC) and compared with the previous Fff using Colebrook -White's Ff as the reference. The study revealed that Ff estimated using the fixed Fff were the same as Ff estimated using Colebrook -White's Fff. The fixed Fff provided the lowest relative error of (0.02 %; 0.06 % and 0.04 % ), the highest MSC (14.03; 12.42 and 13.07); and the lowest AIC (-73006; -64580 and -67982). The study concluded that modeling of Fff using numerical methods and Microsoft Excel Solver are better tools for estimating Ff in pipeline flow problems.

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“…Relative error (RErr) was determined using equation (10) [36] and Ghanbari et al [52]. This result shows that Microsoft Excel Solver can be used to develop Fff for estimating the Ff.…”

Section: Methodsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Accurate solutions of Colebrook-White’s friction factor formulae

Lukman¹,

Oke²

2018

Nig. J. Tech.

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“…It should be taken into account that the Moody diagram cannot be used as a reliable and accurate replacement for the Colebrook equation as its reading error can be even more than few percent [10,34,35]. Using iterative methods, namely, the Newton-Raphson, the friction factor ( ) can be calculated from the Colebrook equation with high accuracy where the convergence of 0.01% requires less than 7 iterations.…”

Section: Definition Of the Problemmentioning

confidence: 99%

Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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Nowadays, the Colebrook equation is used as a mostly accepted relation for the calculation of fluid flow friction factor. However, the Colebrook equation is implicit with respect to the friction factor ( ). In the present study, a noniterative approach using Artificial Neural Network (ANN) was developed to calculate the friction factor. To configure the ANN model, the input parameters of the Reynolds Number (Re) and the relative roughness of pipe ( / ) were transformed to logarithmic scales. The 90,000 sets of data were fed to the ANN model involving three layers: input, hidden, and output layers with, 2, 50, and 1 neurons, respectively. This configuration was capable of predicting the values of friction factor in the Colebrook equation for any given values of the Reynolds number (Re) and the relative roughness ( / ) ranging between 5000 and 10 8 and between 10 −7 and 0.1, respectively. The proposed ANN demonstrates the relative error up to 0.07% which had the high accuracy compared with the vast majority of the precise explicit approximations of the Colebrook equation.

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“…It is valid only for smooth pipes and up to the Reynolds number 10 5 . As cited by Fang et al, (2011) …”

Section: Blasius Correlations (1913)mentioning

confidence: 99%

A comparative study of friction factor correlations for high concentrate slurry flow in smooth pipes

Assefa

Kaushal

2015

Journal of Hydrology and Hydromechanics

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A number of correlations for friction factor determinations in smooth pipes have been proposed in the past decades. The accuracy and applicability of these friction factor formulas should be examined. Based on this notion the paper is designed to provide a comparative study of friction factor correlations in smooth pipes for all flow regimes of Bingham fluids. Nine models were chosen. The comparisons of the selected equations with the existing experimental results, which are available in the literature, were expressed through MARE, MRE + , MRE -, RMSE, Ѳ, and S. The statistical comparisons were also carried out using MSC and AIC. The analyses show that the Wilson-Thomas (1985) and Morrison (2013) models are best fit models to the experimental data for the Reynolds number up to 40000. Within this range, both models can be used alternately. But beyond this Re value the discrepancy of the Wilson-Thomas model is higher than the Morrison model. In view of the fact that the Morrison model requires fewer calculations and parameters as well as a single equation is used to compute the friction factor for all flow regimes, it is the authors' advice to use this model for friction factor estimation for the flow of Bingham fluids in smooth pipes as an alternative to the Moody chart and other implicit formulae.

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New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations

Cited by 242 publications

References 25 publications

Accurate solutions of Colebrook-White’s friction factor formulae

Accurate solutions of Colebrook-White’s friction factor formulae

Intelligent Flow Friction Estimation

A comparative study of friction factor correlations for high concentrate slurry flow in smooth pipes

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