Discussion of “Approximate Analytical Solutions for the Colebrook Equation” by Ali R. Vatankhah
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Volume 146, Issue 2
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Acknowledgments
This work has been supported by the Technology Agency of the Czech Republic through the National Centre for Energy (TN01000007); VŠB–Technical University of Ostrova through the Energy System for Grids program (TK02030039); and the Ministry of Education, Youth, and Sports of the Czech Republic through the National Programme of Sustainability II (NPS II), IT4Innovations Excellence in Science project. (LQ1602).
Disclaimer
The views expressed are those of the authors and may not in any circumstances be regarded as stating an official position of the European Commission or of the Technical University Ostrava. Both authors contributed equally to this discussion.
References
Baker, G. A., and P. Graves-Morris. 1996. “Padé approximants.” In Encyclopedia of mathematics and its applications. Cambridge, UK: Cambridge University Press.
Brkić, D. 2011a. “New explicit correlations for turbulent flow friction factor.” Nucl. Eng. Des. 241 (9): 4055–4059. https://doi.org/10.1016/j.nucengdes.2011.07.042.
Brkić, D. 2011b. “Review of explicit approximations to the Colebrook relation for flow friction.” J. Pet. Sci. Eng. 77 (1): 34–48. https://doi.org/10.1016/j.petrol.2011.02.006.
Brkić, D. 2012. “Determining friction factors in turbulent pipe flow.” Chem. Eng. 119 (3): 34–39.
Brkić, D. 2016. “Spreadsheet-based pipe networks analysis for teaching and learning purpose.” Spreadsheets Educ. (eJSiE) 9 (2): 4.
Brkić, D. 2017a. “Discussion of ‘Exact analytical solutions of the Colebrook-White equation’ by Yozo Mikata and Walter S. Walczak.” J. Hydraul. Eng. 143 (9): 07017007. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001341.
Brkić, D. 2017b. “Solution of the implicit Colebrook equation for flow friction using Excel.” Spreadsheets Educ. (eJSiE) 10 (2): 2.
Brkić, D., and Ž. Ćojbašić. 2016. “Intelligent flow friction estimation.” Comput. Intell. Neurosci. 2016: 5242596. https://doi.org/10.1155/2016/5242596.
Brkić, D., and Ž. Ćojbašić. 2017. “Evolutionary optimization of Colebrook’s turbulent flow friction approximations.” Fluids 2 (2): 15. https://doi.org/10.3390/fluids2020015.
Chen, N. H. 1979. “An explicit equation for friction factor in pipe.” Ind. Eng. Chem. Fundam. 18 (3): 296–297. https://doi.org/10.1021/i160071a019.
Clamond, D. 2009. “Efficient resolution of the Colebrook equation.” Ind. Eng. Chem. Res. 48 (7): 3665–3671. https://doi.org/10.1021/ie801626g.
Ćojbašić, Ž., and D. Brkić. 2013. “Very accurate explicit approximations for calculation of the Colebrook friction factor.” Int. J. Mech. Sci. 67 (Feb): 10–13. https://doi.org/10.1016/j.ijmecsci.2012.11.017.
Colebrook, C. F. 1939. “Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws.” J. Inst. Civil Engineers (London) 11 (4): 133–156. https://doi.org/10.1680/ijoti.1939.13150.
Colebrook, C. F., and C. M. White. 1937. “Experiments with fluid friction in roughened pipes.” Proc. R. Soc. London 161 (906): 367–381. https://doi.org/10.1098/rspa.1937.0150.
Dubčáková, R. 2011. “Eureqa: Software review.” Genet. Program. Evolvable Mach. 12 (2): 173–178. https://doi.org/10.1007/s10710-010-9124-z.
Džunić, J., M. S. Petković, and L. D. Petković. 2011. “A family of optimal three-point methods for solving nonlinear equations using two parametric functions.” Appl. Math. Comput. 217 (19): 7612–7619. https://doi.org/10.1016/j.amc.2011.02.055.
Giustolisi, O., L. Berardi, and T. M. Walski. 2011. “Some explicit formulations of Colebrook–White friction factor considering accuracy vs. computational speed.” J. Hydroinf. 13 (3): 401–418. https://doi.org/10.2166/hydro.2010.098.
Gregory, G. A., and M. Fogarasi. 1985. “Alternate to standard friction factor equation.” Oil Gas J. 83 (13): 120–127.
Mikata, Y., and W. S. Walczak. 2016. “Exact analytical solutions of the Colebrook-White equation.” J. Hydraul. Eng. 142 (2): 04015050. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001074.
Özger, M., and G. Yıldırım. 2009. “Determining turbulent flow friction coefficient using adaptive neuro-fuzzy computing technique.” Adv. Eng. Software 40 (4): 281–287. https://doi.org/10.1016/j.advengsoft.2008.04.006.
Schmidt, M., and H. Lipson. 2009. “Distilling free-form natural laws from experimental data.” Science 324 (5923): 81–85. https://doi.org/10.1126/science.1165893.
Schorle, B. J., S. W. Churchill, and M. Shacham. 1980. “Comments on: ‘An explicit equation for friction factor in pipe’.” Ind. Eng. Chem. Fundam. 19 (2): 228–230. https://doi.org/10.1021/i160074a019.
Serghides, T. K. 1984. “Estimate friction factor accurately.” Chem. Eng. (New York) 91 (5): 63–64.
Sharma, J. R., and H. Arora. 2016. “A new family of optimal eighth order methods with dynamics for nonlinear equations.” Appl. Math. Comput. 273 (Jan): 924–933. https://doi.org/10.1016/j.amc.2015.10.049.
Sonnad, J. R., and C. T. Goudar. 2006. “Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook–White equation.” J. Hydraul. Eng. 132 (8): 863–867. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(863).
Vatankhah, A. R. 2014. “Comment on ‘Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation.’” J. Pet. Sci. Eng. 124 (Dec): 402–405. https://doi.org/10.1016/j.petrol.2013.12.001.
Vatankhah, A. R., and S. Kouchakzadeh. 2008. “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.” J. Hydraul. Eng. 134 (8): 1187. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:8(1187).
Vatankhah, A. R., and S. Kouchakzadeh. 2009. “Discussion: Exact equations for pipe-flow problems.” J. Hydraul. Res. 47 (4): 537–538. https://doi.org/10.1080/00221686.2009.9522031.
Winning, H. K., and T. Coole. 2013. “Explicit friction factor accuracy and computational efficiency for turbulent flow in pipes.” Flow, Turbul. Combust. 90 (1): 1–27. https://doi.org/10.1007/s10494-012-9419-7.
Zigrang, D. J., and N. D. Sylvester. 1982. “Explicit approximations to the solution of Colebrook’s friction factor equation.” AlChE J. 28 (3): 514–515. https://doi.org/10.1002/aic.690280323.
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Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Apr 10, 2018
Accepted: Jun 1, 2018
Published online: Nov 20, 2019
Published in print: Feb 1, 2020
Discussion open until: Apr 20, 2020
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