Discussions and Closures
Jun 15, 2017

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 ARTICLE
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 9
First page of PDF

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

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 143Issue 9September 2017

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

Permissions

Request permissions for this article.

Authors

Affiliations

Dejan Brkić, Ph.D. [email protected]
Research Fellow, European Commission, DG Joint Research Center, Institute for Energy and Transport, Energy Security, Systems and Market Unit, Via Enrico Fermi 2749, Ispra (VA), Italy. E-mail: [email protected]; [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share