Numerical Solution of two-dimensional velocity Distribution in Straight Compound channels

In the river, velocity parameter is one of the most important hydraulic variables and is effectively used in many river engineering fields like development of stage-discharge curve and sediment transport. In some river engineering schemes, the calculation of average flow velocity is sufficient. However, for some other projects, such as designing hydraulic structures in the river, stable channel design, flood calculations in rivers and floodplains, the lateral and vertical distributions of flow velocity should be calculated. To calculate the two-dimensional distribution of the velocity of flow (in transverse and vertical directions) many mathematical models have been presented with many complexities from practical point of view. In this research, a simple and practical mathematical model of Kean et al in combination with eddy viscosity equation as well as Einstein's law of the wall velocity was used to determine the two-dimensional flow velocity distribution in the smooth and rough compound channels. By numerical solution of this mathematical model, using finite differences method, isovel curves data were calculated for some experimental compound channels with different flow depths and floodplain's roughness coefficients and then they were compared with the experimental data. Also, transverse distributions of the flow velocity were calculated in these channels and compared with the measured profiles. These comparisons showed that the proposed mathematical model with coefficient of determination (R2)= 0.92, root-mean-square error (RMSE)=0.036 and mean absolute percentage error (MAPE)= 2.8% had an acceptable accuracy. The proposed mathematical model was developed with steady and uniform flow assumption, neglecting the secondary flow effect.