A numerical solution for depth-averaged velocity distribution in an open channel flow

The complexity of two-dimensional SKM model is to calibrate the three governing parameters (bed friction f, eddy viscosity coefficient λ or turbulent friction and secondary flow Г) before it can be applied to predict the depth-averaged velocity in an open channel flow. To quantify the secondary current, the factor k needs to be calibrated from reliable data-sets. The roughness parameter f is considered from the surface properties of the channel, whereas the eddy viscosity parameter λ is generally taken to be constant value. A computer program has been developed to solve the two-dimensional SKM model analytically so as to simulate the depth-averaged velocities from point to point along the lateral directions. The results reveal that the secondary flow factor k bears a specific relationship with flow depths over the constant depth domain and another relationship for variable depth domain. In this study, mathematical relationships have also been developed for accurate estimation of secondary flow coefficients for constant flow depth domain and variable flow depth domain of an open channel flow under different flow conditions which cover the ranges of Reynolds number from 7808 to 369,000 and geometry conditions with aspect ratio ranging from 5 to 30.