Improved explicit equations for estimation of the friction factor in rough and smooth pipes

Romeo, E.; Royo, C.; Μοnzόn, A.

doi:10.1016/s1385-8947(01)00254-6

Cited by 182 publications

(162 citation statements)

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“…In the study conducted by Brkić [6], it was concluded that the five most available approximations from the literature had the maximum relative error up to 0.15%. These approximations were suggested by Zigrang and Sylvester [46], Serghides [42], Romeo et al [43], Buzzelli [45], and Vatankhah and Kouchakzadeh [44] (even more accurate approximations are shown in Vatankhah [50] where their accuracy is comparable with accuracy of approximations shown inĆojbašić and Brkić [37]). Furthermore,Ćojbašić and Brkić [37] applied genetic algorithm optimization technique (also genetic technique are used in [51,52]).…”

Section: Comparative Analysismentioning

confidence: 75%

“…Furthermore,Ćojbašić and Brkić [37] applied genetic algorithm optimization technique (also genetic technique are used in [51,52]). This technique improved two of these accurate approximations suggested by Serghides [42] and Romeo et al [43] to reach even extreme level of accuracy with the relative error up to 0.0026% and 0.0083%, respectively. All mentioned explicit approximations are listed in Appendix of this paper (they are also attached to this paper as Electronic Appendix C (PDF file with all approximations of the Colebrook equation mentioned through text with their MATLAB codes and MS Excel codes)).…”

Section: Comparative Analysismentioning

confidence: 81%

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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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Section: Comparative Analysismentioning

confidence: 75%

Section: Comparative Analysismentioning

confidence: 81%

Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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“…Ćojbašić and Brkić [42] already optimized numerical values of parameters by Romeo et al [27] and by Serghides [30].…”

Section: Explicit Approximations Of Colebrook's Equationmentioning

confidence: 99%

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Brkić¹,

Ćojbašić²

2017

Preprint

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Today, Colebrook's equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook's equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook's equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook's equation and its Moody's plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

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“…Para escoamento em tubos comerciais rugosos é a equação mais utilizada para calcular , 1976;SERGHIDES, 1984;PORTO, 1998;ROMEO et al, 2002;YOO;SINGH, 2005;SONNAD;GOUDAR, 2006).…”

Section: Lista De Tabelasunclassified

Perda de carga em conectores iniciais da irrigação localizada

Vilaça¹

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Improved explicit equations for estimation of the friction factor in rough and smooth pipes

Cited by 182 publications

References 9 publications

Intelligent Flow Friction Estimation

Intelligent Flow Friction Estimation

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Perda de carga em conectores iniciais da irrigação localizada

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Improved explicit equations for estimation of the friction factor in rough and smooth pipes

Cited by 182 publications

References 9 publications

Intelligent Flow Friction Estimation

Intelligent Flow Friction Estimation

Evolutionary Optimization of Colebrook&rsquo;s Turbulent Flow Friction Approximations

Perda de carga em conectores iniciais da irrigação localizada

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Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations