Discussion of “Exact Analytical Solutions of the Colebrook-White Equation” by Yozo Mikata and Walter S. Walczak
This article is a reply.
VIEW THE ORIGINAL ARTICLEPublication: Journal of Hydraulic Engineering
Volume 143, Issue 9
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Disclaimer
Neither the European Commission nor any person acting on behalf of it is responsible for the use which might be made of this publication.
References
Barry, D. A., Parlange, J. Y., Li, L., Prommer, H., Cunningham, C. J., and Stagnitti, F. (2000). “Analytical approximations for real values of the Lambert W-function.” Math. Comput. Simul., 53(1–2), 95–103.
Boyd, J. P. (1998). “Global approximations to the principal real-valued branch of the Lambert W-function.” Appl. Math. Lett., 11(6), 27–31.
Brkić, D. (2011a). “An explicit approximation of the Colebrook equation for fluid flow friction factor.” Petrol. Sci. Tech., 29(15), 1596–1602.
Brkić, D. (2011b). “New explicit correlations for turbulent flow friction factor.” Nucl. Eng. Des., 241(9), 4055–4059.
Brkić, D. (2011c). “Review of explicit approximations to the Colebrook relation for flow friction.” J. Petrol. Sci. Eng., 77(1), 34–48.
Brkić, D. (2011d). “W solutions of the CW equation for flow friction.” Appl. Math. Lett., 24(8), 1379–1383.
Brkić, D. (2012a). “Can pipes be actually really that smooth?” Int. J. Refrig., 35(1), 209–215.
Brkić, D. (2012b). “Comparison of the Lambert W-function based solutions to the Colebrook equation.” Eng. Comput., 29(6), 617–630.
Brkić, D. (2012c). “Determining friction factors in turbulent pipe flow.” Chem. Eng., 119(3), 34–39.
Brkić, D., and Ćojbašić, Ž. (2016). “Intelligent flow friction estimation.” Comput. Intell. Neurosci., 2016, 1–10.
Brkić, D., and Ćojbašić, Ž. (2017). “Evolutionary optimization of colebrook’s turbulent flow friction approximations.” Fluids, 2(2), 27.
Clamond, D. (2009). “Efficient resolution of the Colebrook equation.” Ind. Eng. Chem. Res., 48(7), 3665–3671.
Ćojbašić, Ž., and Brkić, D. (2013). “Very accurate explicit approximations for calculation of the Colebrook friction factor.” Int. J. Mech. Sci., 67, 10–13.
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 Eng., 11(4), 133–156.
Colebrook, C. F., and White, C. M. (1937). “Experiments with fluid friction in roughened pipes.” Proc. R. Soc. Ser. A Math. Phys. Sci., 161(906), 367–381.
Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., and Knuth, D. E. (1996). “On the Lambert W-function.” Adv. Comput. Math., 5(1), 329–359.
Giustolisi, O., Berardi, L., and Walski, T. M. (2011). “Some explicit formulations of Colebrook-White friction factor considering accuracy versus computational speed.” J. Hydroinf., 13(3), 401–418.
Goudar, C. T., and Sonnad, J. R. (2003). “Explicit friction factor correlation for turbulent flow in smooth pipes.” Ind. Eng. Chem. Res., 42(12), 2878–2880.
Hayes, B. (2005). “Why W?” Am. Sci., 93(2), 104–108.
Keady, G. (1998). “Colebrook-White formula for pipe flow.” J. Hydraul. Eng., 96–97.
Rollmann, P., and Spindler, K. (2015). “Explicit representation of the implicit Colebrook-White equation.” Therm. Eng., 5, 41–47.
Sonnad, J. R., and Goudar, C. T. (2004). “Constraints for using Lambert W function-based explicit Colebrook-White equation.” J. Hydraul. Eng., 929–931.
Sonnad, J. R., and Goudar, C. T. (2006). “Turbulent flow friction factor calculation using a mathematically exact alternative to the Colebrook-White equation.” J. Hydraul. Eng., 863–867.
Winitzki, S. (2003). “Uniform approximations for transcendental functions.” Int. Conf. on Computational Science and Its Applications—ICCSA 2003, Proc., Lecture Notes in Computer Science, Springer, Berlin, 780–789.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Dec 22, 2015
Accepted: Aug 9, 2016
Published online: Jun 15, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 15, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.