Critical and Normal Depths in Semielliptical Channels

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.