Critical and Normal Depths in Semielliptical Channels
Publication: Journal of Irrigation and Drainage Engineering
Volume 141, Issue 10
Abstract
Normal and critical epths are important parameters in the design, operation, and maintenance of open channels. Semielliptical, prefabricated channels are widely used as tertiary canals in irrigation networks. In semielliptical channels, the governing equations are highly nonlinear in the normal and critical flow depths; thus, the solution of the implicit equations involves numerical methods. The main challenge with semielliptical sections is the calculation of the wetted perimeter. The wetted perimeter of semielliptical sections can be expressed in terms of incomplete elliptic integrals of the second kind. The elliptic integrals can be computed simply using commercial mathematical software, but most engineers who use a simple tool such as Microsoft Excel need a simple yet accurate expression for computing the wetted perimeter. Because elliptic integrals cannot be directly computed using Excel, a simple and accurate expression with maximum error less than 0.07% (near exact solution) is proposed for computing the wetted perimeter. In this study, explicit solutions for semielliptical channels have also been obtained using the nondimensional forms of the governing equations. The maximum errors of critical and normal flow depths are less than 0.1%. Proposed explicit equations have high accuracy, easy calculation, and wide application range.
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Acknowledgments
The author gratefully acknowledges the support provided by the Center of Excellence for Evaluation and Rehabilitation of Irrigation and Drainage Networks, University of Tehran.
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© 2015 American Society of Civil Engineers.
History
Received: Sep 11, 2014
Accepted: Jan 22, 2015
Published online: Feb 24, 2015
Discussion open until: Jul 24, 2015
Published in print: Oct 1, 2015
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