Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar

Vatankhah, Ali R.; Kouchakzadeh, S.

doi:10.1061/(asce)0733-9429(2008)134:8(1187)

Cited by 34 publications

(31 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: 77%

“…In addition, the suggested ANN structure in this study might be used with the most accurate explicit approximations of the Colebrook equation implied byĆojbašić and Brkić [37] Sylvester [46], and Vatankhah and Kouchakzadeh [44]. The maximum relative errors for these approximations were evaluated to be 0.0026%, 0.13%, 0.14%, 0.14%, 0.14%, and 0.15%, respectively.…”

Section: Comparative Analysismentioning

confidence: 99%

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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: 77%

Section: Comparative Analysismentioning

confidence: 99%

Intelligent Flow Friction Estimation

Brkić¹,

Ćojbašić²

2017

Preprint

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“…Also, approximations by Buzzelli (2008) and Serghides (1984) or by Zigrang and Sylvester (1982) are very accurate with an error of no more than 0.1385%. Vatankhah and Kouchakzadeh (2008) also show very accurate approximation with a relative error up to 0.1472%. There are at least ten approximations more accurate than the SwameeJain equation.…”

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confidence: 72%

Discussion of “Jacobian Matrix for Solving Water Distribution System Equations with the Darcy-Weisbach Head-Loss Model” by Angus Simpson and Sylvan Elhay

Brkić

2012

J. Hydraul. Eng.

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“…Additionally, curve fitting or surface fitting tool from Matlab can be used for fine tuning of coefficients after improvements made using genetics algorithm optimization techniques [23 , 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 9 24]. Using only fitting tool of Matlab (with no use of genetic algorithms), Vatankhah and Kouchakzadeh [23,24] improved coefficients from the approximation of Sonnad and Goudar [32,33] (in that way maximal relative error decrease from 0.8003% to 0.1472%).…”

Section: Resultsmentioning

confidence: 99%

Very accurate explicit approximations for calculation of the Colebrook friction factor

Ćojbašić

Brkić

2013

International Journal of Mechanical Sciences

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Along with the revised version R2 of the manuscript IJMS-111051R2 by Ž. Ćojbašid and D. Brkid which is submitted through online system, enclosed please find responses to the comments of the reviewers to the previous revised version R1 of the paper.First of all, authors would like to express their gratitude to you, professor Reid and the reviewers for valuable comments and remarks along the review process, which helped us to improve the paper quality.Althoug reviewer #1 had no further suggestions and reviewer #2 suggested minor improvements (at the same time proposing positive decision and not demanding that paper is further returned to him), every effort has been made to fully embrace the final recommendations. Comments of the ANSWER:The mentioning of MS Excel was motivated by our previous paper regarding usage of this software for efficient Colebrook friction factor calculation. However, we approved reviewer's opinion and to avoid any confusion among the readers we have deleted text in brackets in sentence on page 3 -'(additionally, λ and λ 0 were evaluated in MS Excel [9])'. POINT 2: Page 4, line 41-56: it is still not clear which kind of distribution of sampling point the authors considered. They state that a uniform distribution could be misleading but do not actually declare their sampling strategy.ANSWER: This has been further clarified by adding explicit statement regarding sampling of the points in the input space defined by the domains of input variables. Text now includes the following sentence altered from R1 verson of the paper: "This area is covered with 740 points uniformly sampled over the ranges of input variables, which means that estimated error can be slightly above (somewhere among four adjacent tested points of the matrix which consists of 740 points)." POINT 3: Finally, the concluding section contains two timed the reference to Giustolisi et al. [22]. In my previous comments I just noticed some discrepancy with actual paper content but it was not my intention to emphasize that paper everywhere through the text. I suggest to move the last sentence of conclusions to the introductory section where it would fit better.ANSWER: Last sentence of the conclusion has been moved to introductory part of the paper. We hope that you will find that we have provided paper improvements that were suggested and we are looking forward to hearing from you soon and publishing of our paper. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 presented, based on already existing models which are improved using genetic algorithms optimization. They are with the maximal relative error of no more than 0.0083% and 0.0026%. POINT 4: Authors' answer to my question (POINT Yours sincerely, Authors

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Discussion of “Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation” by Jagadeesh R. Sonnad and Chetan T. Goudar

Cited by 34 publications

References 0 publications

Intelligent Flow Friction Estimation

Intelligent Flow Friction Estimation

Discussion of “Jacobian Matrix for Solving Water Distribution System Equations with the Darcy-Weisbach Head-Loss Model” by Angus Simpson and Sylvan Elhay

Very accurate explicit approximations for calculation of the Colebrook friction factor

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