Direct integration of gradually varied flow equation in parabolic channels

The direct integration method is used to compute water surface profiles of gradually varied flow (GVF) in a prismatic open channel. No closed-form solution is available for the GVF equation in the case of general parabolic channels. Open channels with parabolic cross-sections are often a quite good approximation of the real geometry of natural rivers. Technology is also available for constructing this shape of channels. In the present study, by applying the Manning formula, a semi-analytical solution to compute the length of the gradually-varied-flow profile for parabolic channels is developed. The proposed solution uses a single step for the computation of water surface profiles and, as such, provides an accurate and yet simple way to compute GVF flow profiles; thus, it should be of interest to practitioners in the hydraulic engineering community.

Figure optionsDownload as PowerPoint slideHighlights
► A semi-analytical solution of the GVF equation for parabolic channels has presented.
► The proposed near-exact solution uses a single step for the profile computation.
► Also provides more efficient calculation procedure compared with other numerical methods.
► The proposed approach may be a leading tool in addressing similar integration solutions.