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This paper aims at the investigation and analysis of numerical and laboratory modelling of flow in branched channels with symmetrical geometry and varying hydraulic conditions. Details of velocity and water-level profiles in branching locations are discussed. In some low-slop regions like plains, rivers may be branching; or in alluvial plains where the slop is low, meanders may appear. On the other hand, in the mountainous and semi-mountainous areas with relatively steep slops, arterial rivers can be formed. Therefore, it is important to learn the behaviour of rivers in branching location and to simulate water flow in branching part of rivers.Details of two-dimensional numerical model in a main channel and secondary downstream branches are explained and results are analysed and compared against experimental data. With respect to the numerical simulation, velocity and depth in different sections of laboratory model are calculated and the corresponding profiles are developed. The water-level profiles are calculated and drawn using both the numerical and experimental models. Some long narrow eddies are predicted along internal bank of junction. The comparison of numerical and experimental models proves reasonable results for this research.

This paper introduces an improved formula for the bed-shear stress by applying the vorticity effect and its application in a 3D flow and sediment model to estimate scouring around bridge piers. Up to now, the sediment transport formulae used for computing pier scour were developed based on the general scouring in unobstructed flow. The capability for numerical models to predict local scour around bridge piers was severely restricted by the sediment transport formulae. The new formula introduced in this paper can take into account vortices that affect the local scour process by adding some terms into the classic bed-shear stress equation.The 3D numerical model system used in this study consists of three modules: (a) an unsteady hydrodynamic module; (b) a sediment transport module; and (c) a Fation module. The hydrodynamic module is based on the 3D RANS equations. The sediment transport module is comprised of semi empirical models of suspended load and non-equilibrium bed load. The bed-deformation module is based on the mass balance for sediment.The model was used to simulate pier scour in tree different test cases: (1) a circular pier;(2) a square pier; and (3) a rectangular pier, by applying the ordinary sediment equation and the newly introduced sediment equation. Results of both numerical simulations were compared against laboratory measured data and also in case 1 with result of Olsen and Melaaen (J. Hydraul. Eng. 1993; 119(9):1048-1054). Comparisons show that the new sediment formula could predict the scour more accurately than the ordinary one.