To investigate the influence laws of the width-to-depth ratio and the radius-to-width ratio on the hydrodynamic characteristics of open-channel bends, this study established a three-dimensional numerical model based on the RNG k-ε turbulence model and the volume of fluid (VOF) free surface tracking method. Numerical simulations of bend flow under four width-to-depth ratios and four radius-to-width ratios were conducted, with a focus on analyzing hydrodynamic characteristics such as water surface profiles, velocity distribution, secondary flows, and bend separation flows. The results indicate that the flow turbulence characteristics intensify as the width-to-depth ratio or radius-to-width ratio decreases. With the reduction of these ratios, flow redistribution becomes increasingly significant, circulation strength strengthens, and the probability of flow separation in bends increases. For the U-shaped bends with small width-to-depth and radius-to-width ratios simulated in this study, the critical conditions for flow separation are identified as a width-to-depth ratio of 1.5 and a radius-to-width ratio of 1.0.