Formulation and solution of the problem of determining erosion and deposition in open channels for loose soils

Flows of water and of the solid particles suspended in them are considered in a one-dimensional approximation and a formulation and solution of the problem of erosion and deposition in open channels are given for the case of loose soils. The effects of friction in the hydrodynamic equations are represented using the classical approach without invoking the concepts of a hydraulic radius and a Chézy coefficient. The rate of erosion and deposition are related to the flow parameters, and the effect of erosion and deposition on the hydrodynamic flow parameters is demonstrated. A theoretical description of this phenomenon, which is due to the removal of solid particles from the surface of the bottom into the flow and their deposition from the flow onto the bottom, is given. An example of a numerical calculation of the erosion and deposition in the case of the corresponding flow parameters is presented. The relations obtained enable the phenomena of erosion and deposition to be analysed both in the one-dimensional and the two-dimensional approximations.