A model has been created for calculating the balanced diversion ratios of flow rate and sediment in the branches of a bifurcated river. The model is based on the extremity law of energy dissipation rate, and involves solving the simultaneous equations of flow and sediment motion for uniform flow in an open channel. The model has been verified by measured data obtained from the Meizizhou and Baguazhou branches of the Yangtze River in China. The parameters that influence the diversion ratios, such as river width, channel roughness and the total inflow, have been analysed. It was found that balanced diversion ratios are more sensitive to river width and roughness than to total inflow. Measures to regulate the Baguazhou branch have been compared further and analysed. The conclusions of this study can provide a theoretical basis for future regulation of the Baguazhou river branch.