The equilibrium relations for water and sediment transport in the Yellow River help manage sediment by balancing sediment transport and stabilizing river courses. By studying sediment carrying capacity and riverbed evolution, researchers established equilibrium relationships for different parts of the Yellow River. They found that in certain areas, erosion and deposition in riverbeds adjust automatically, forming stable relationships between water and sediment transport. These new equilibrium relationships can be used to plan the best way to distribute sediment in the Yellow River.