In this article the mathematical model of unsteady flow the two-phase open stream taking into account the redistribution of the particulate concentration, the depth of flow and water filtration on the bottom of the channel, and also created an efficient method of calculation. In this case, the two-speed flow is considered, i.e. the presence of the longitudinal and vertical components of the phase velocities is taken into account, and we also believe that the flow parameters along the flow do not change. Initial and boundary conditions are established based on theoretical and empirical formulas, which are widely used in practice. The flow in open channels is non-pressurized, occurs under the influence of gravity and is characterized by the fact that the flow has a free surface. At the initial moment of time, we consider the flow to be uniform in the longitudinal direction and all parameters are set by known theoretical and empirical formulas. At the bottom of the channel for longitudinal velocity component of the water use condition of adhesion, and for the longitudinal velocity component of solid phase condition for the shift and believe the known concentrations of solid particles, and vertical components of velocity the phases of the filtering conditions (for water), and hydraulic size (for solid particles). On the free surface, we consider that there are no solid particles, and for the longitudinal components of the phase velocities we neglect the force of air friction, and for the vertical components of the phase velocities we use the condition of non-uniformity of the free surface in time. On the basis of the developed mathematical model and the created method of calculation, the changes of the main parameters in the depth of the flow and in time are determined.
Simultaneous imaging of two-phase velocities in particle-laden flows by two-color optical phase discrimination
