Abstract
Existing entropy-based methodologies for deriving two-dimensional (2D) velocity distributions in open-channel flow are based on the extension of one-dimensional (1D) formulations. Such extensions contain too many parameters and require either experimental calibration or that velocity be known at several points. This information is not always available or does not apply under some particular conditions. Following the approach developed for a rectangular cross section, this paper develops an entropy-based method for deriving a 2D velocity distribution for a generic-shaped cross section. The derived distribution is parsimonious and can be applied to natural watercourses, which usually do not have a regular cross section. The model is consistent with previous results because the velocity distribution for a simple domain can be derived as a particular case of a more complex domain. The method was validated against velocity data collected in almost 200 data series along three rivers. The velocities calculated by the new method were found to be in good agreement with measured data. The results were also compared with two methods available in the literature. One of these methods showed better performance than the proposed model, although it requires much more information.
Get full access to this article
View all available purchase options and get full access to this article.
References
Chiu, C. L. (1987). “Entropy and probability concepts in hydraulics.” J. Hydraul. Eng., 583–599.
Chiu, C. L. (1988). “Entropy and 2-D velocity distribution in open channels.” J. Hydraul. Eng., 738–756.
Chiu, C. L. (1989). “Velocity distribution in open channel flow.” J. Hydraul. Eng., 576–594.
Chiu, C. L., and Said, C. A. (1995). “Maximum and mean velocities and entropy in open-channel flow.” J. Hydraul. Eng., 26–35.
Chiu, C. L., and Tung, N. C. (2002). “Maximum velocity and regularities in open-channel flow.” J. Hydraul. Eng., 390–398.
Fontana, N., Marini, G., and De Paola, F. (2013). “Experimental assessment of a 2-D entropy-based model for velocity distribution in open channel flow.” Entropy, 15(3), 988–998.
Giugni, M., Fontana, N., Lombardi, G., and Marini, G. (2008). “Surface waters vulnerability and minimum instream flow assessment: An Italian case study.” Proc., 13th IWRA World Water Congress 2008, French Ministry of Foreign and European Affairs and the Ministry of High Education and Research, Montpellier, France.
Jaynes, E. T. (1957). “Information theory and statistical mechanics.” Phys. Rev., 106(4), 620–630.
Kapur, J. N. (1989). Maximum-entropy models in science and engineering, Wiley, Hoboken, NJ.
Krause, P., Boyle, D. P., and Base, F. (2005). “Comparison of different efficiency criteria for hydrological model assessment.” Adv. Geosci., 5(1), 89–97.
Marini, G., De Martino, G., Fontana, N., Fiorentino, M., and Singh, V. P. (2011). “Entropy approach for 2D velocity distribution in open channel flow.” J. Hydraul. Res., 49(6), 784–790.
Moramarco, T., Saltalippi, C., and Singh, V. P. (2004). “Estimation of mean velocity in natural channels based on Chiu’s velocity distribution equation.” J. Hydrol. Eng., 42–50.
Moramarco, T., Saltalippi, C., and Singh, V. P. (2011). “Velocity profiles assessment in natural channels during high floods.” Hydrol. Res., 42(2–3), 162–170.
Shannon, C. E. (1948). “A mathematical theory of communication.” Bell Syst. Tech. J., 27(3), 379–423.
Singh, V. P. (2011). “Derivation of power law and logarithmic velocity distributions using the Shannon entropy.” J. Hydrol. Eng., 478–483.
Singh, V. P., Marini, G., and Fontana, N. (2013). “Derivation of 2D power-law velocity distribution using entropy theory.” Entropy, 15(4), 1221–1231.
Singh, V. P., Yang, C. T., and Deng, Z. Q. (2003). “Downstream hydraulic geometry relations. 1: Theoretical development.” Water Resour. Res., 39(12), 1–15.
Tang, X., and Knight, D. W. (2009). “Analytical models for velocity distributions in open channel flows.” J. Hydraul. Res., 47(4), 418–428.
Yang, C. T. (1972). “Unit stream power and sediment transport.” J. Hydraul. Div., 98(HY10), 1805–1826.
Yang, C. T. (1976). “Minimum unit stream power and fluvial hydraulics.” J. Hydraul. Div., 102(HY7), 919–934.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 22 • Issue 6 • June 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Mar 24, 2016
Accepted: Oct 14, 2016
Published online: Feb 17, 2017
Published in print: Jun 1, 2017
Discussion open until: Jul 17, 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.