Modeling of Unsteady Flow through the Canals by Semiexact Method

Abstract

The study of free-surface and pressurized water flows in channels has many interesting application, one of the most important being the modeling of the phenomena in the area of natural water systems (rivers, estuaries) as well as in that of man-made systems (canals, pipes). For the development of major river engineering projects, such as flood prevention and flood control, there is an essential need to have an instrument that be able to model and predict the consequences of any possible phenomenon on the environment and in particular the new hydraulic characteristics of the system. The basic equations expressing hydraulic principles were formulated in the 19th century by Barre de Saint Venant and Valentin Joseph Boussinesq. The original hydraulic model of the Saint Venant equations is written in the form of a system of two partial differential equations and it is derived under the assumption that the flow is one-dimensional, the cross-sectional velocity is uniform, the streamline curvature is small and the pressure distribution is hydrostatic. The St. Venant equations must be solved with continuity equation at the same time. Until now no analytical solution for Saint Venant equations is presented. In this paper the Saint Venant equations and continuity equation are solved with homotopy perturbation method (HPM) and comparison by explicit forward finite difference method (FDM). For decreasing the present error between HPM and FDM, the st.venant equations and continuity equation are solved by HAM. The homotopy analysis method (HAM) contains the auxiliary parameter ħ that allows us to adjust and control the convergence region of solution series. The study has highlighted the efficiency and capability of HAM in solving Saint Venant equations and modeling of unsteady flow through the rectangular canal that is the goal of this paper and other kinds of canals.