Exact Solution of Optimum Hydraulic Power-Law Section with General Exponent Parameter
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VIEW THE REPLYPublication: Journal of Irrigation and Drainage Engineering
Volume 144, Issue 12
Abstract
Power-law sections provide great flexibility in open channel design. However, in the literature the optimum hydraulic power-law section has been developed for only specific values of the exponent of the power-law formula. This paper presents a general exact solution of the optimum hydraulic section with as a parameter based on Gaussian hypergeometric mathematics and the Lagrange multiplier method. The relationships between and each of the optimum width-depth ratio and the side slope are derived. The explicit exact formulas of the shape factor, normal depth, critical depth, discharge, wetted perimeter, and flow area for different values are presented. The results show that the discharge of the optimum hydraulic section increases as and then decreases as for a given flow area or wetted perimeter. In addition, a super-best hydraulic power-law section with exists, where the discharge is largest. This super-best section represents a new discovery as it provides the global maximum discharge among all possible power-law section shapes. The characteristics of the super-best section are presented.
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Acknowledgments
The authors are grateful to the editors and five anonymous reviewers for their thorough and most helpful comments. This research project is supported by the Natural Science Foundation of Shandong Province, China (ZR2017LEE028), the Key Research and Development Program of Shandong Province, China (2016GSF117038), the National Science and Technology Support Program of China (2015BAB07B02), the Development of Science and Technology Plan of Jinan City, China (201302052), and the Teaching and Research Projects of the University of Jinan (J1641).
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©2018 American Society of Civil Engineers.
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Received: May 19, 2017
Accepted: Jul 16, 2018
Published online: Oct 9, 2018
Published in print: Dec 1, 2018
Discussion open until: Mar 9, 2019
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