Analytical Integration of Gradually Varied Flow in Open Channel without Varied-Flow Function

The direct-integration method is a general method used to solve analytically the gradually-varied-flow (GVF) equation. This study has summarized previous works to find the direct integration solutions of the GVF equation by using the varied-flow functions (VFF). The GVF solution by the Bakhmeteff-Chow procedure can be obtained with VFF-tables. These VFF-tables needed in the direct-integration method has a drawback caused by the imprecise interpolation of the VFF-values. To overcome this drawback, it can be solved directly the GVF equation without VFF in this study. Of course, in order to avoid calculation complexity, we use the Chezy formula which is the simplest form of the GVF equations in a wide open channel. The analytical solution derived in this study is exactly identical to that by Bresse (1868).