A Mathematical Model of Water and Sediment Flow in Open River Channels

M. V. Shmakova and A. N. Kondrat’ev

Aone-dimensional mathematical model of water and sediment flow in open channels is proposed based on the forces influencing a water stream and bottom and stream sediments. The equations of water and sediment flow are closed by the equations of continuity of stream, velocity of particle motion in a stream, and the equation of balance of kinetic energy and moving particles: joint calculation of stream hydraulic characteristics and sediment discharge is performed. Hydraulic resistances are retrieved not from the Chezi formula, but based on the balance of forces and kinetic energy. A sediment discharge is calculated from velocities and the number of moving solid particles instead of empirical relationships whose accuracy is usually low. The model is verified against the data of experiments in hydraulic flumes with glass and sand bottom. Comparison with independent data in the glass flume in a wide range of water discharges and bottom inclinations showed a high accuracy of calculation of hydraulic characteristics (relative error is less than 4%). The experimental data showed that the accuracy of sediment discharge calculated by the model exceeds the accuracy of the calculation using traditional empirical formulas.