Use of the Gaussian hypergeometric function to solve the equation of gradually-varied flow

The direct-integration method is a conventional method used to analytically solve the equation of gradually-varied flow (GVF) that is a steady non-uniform flow in an open channel with gradually changes in its water surface elevation. The GVF equation is normalized by using the normal depth h(n). The varied-flow function (VFF) needed in the direct-integration method has a drawback caused by the imprecise interpolation of the VFF-values. To overcome the drawback, we successfully use the Gaussian hypergeometric function (GHF) to analytically solve the GVF equation without recourse to the VFF in the present paper. The GHF-based solutions can henceforth play the role of the VFF table in the interpolation of the VFF-values. We plot the GHF-based solutions for GVF profiles in the mild (M), critical (C), and steep (S) wide channels under specific boundary conditions, thereby analyzing the effects of the dimensionless critical depth h(c)/h(n) and the hydraulic exponent N-value on the profiles. (C) 2012 Elsevier B.V. All rights reserved.