A 2-D Model simulating the flow behavior to solve local hydraulic problems in rivers

A Quasi-steady flow in rivers has been considered with the objective of determining the flow patterns which are important in solving the navigation difficulties and other local hydraulicproblems in rivers. The approach used for simulating the flow hasbased on what is referred to as the ”Shallow-Water” approximation.// The two-dimens ional hydrodynamics (i. e . mass andbalance) equations have been solved using a time-dependent momentum finitedifference method. The numerical solution is utilized thevorticity-transport and stream-function approach. The forward time centered space method has been used for solving the vorticity transport equation while the successive over relaxation method has been used for solving the stream function equation.The developed two-dimensional mathematical model has been verified using detailed laboratory as well as field measurements.Different reaches of the Nile River have been considered forverification. A faire agreement is found. In addition, the presentmathematical model has been applied for solving navigation difficulties actually existed at three reaches of the Nile River.Different proposals for the navigation trenches have been suggested and the safest one has been recommended for each case study.