Shallow water flow down an inclined open channel: analytical solutions of governing equations .

Abstract

In this paper we consider a problem of a fluid flow with free surface in variable turbulent mode in a long inclined open channel, taking into account the Chezy drag. We have obtained a family of exact solutions for the governing equations, i.e. a family of velocity and height fields of water above the channel bed. Moreover, we have estimated the extremum of the water height. These results can be used as essential tools for the planning and management for sustainable use of water resources( the drainage of surface waters or irrigation water of the soil in agriculture and so on).