Abstract: Water depth and critical water depth are crucial hydraulic factors in the study, design, and operation management of water conveyance tunnels. The computation of the characteristic water level for a circular hydraulic section is crucial in determining the ideal section for hydraulic purposes. To address the limitations of existing formulas in terms of accuracy and applicability, we have developed several functional models based on the fundamental equation of flow motion, using characteristic parameters of flow cross section, dimensionless depth, and the concept of limit thinking in mathematical operations. The enhanced particle swarm optimization（PSO） is employed in lieu of conventional parameter determination to ascertain a simplified formula for the calculation of characteristic water depth of non-pressure flow in a circular tunnel. Comparative analysis with typical formulas demonstrates that the proposed formula exhibits a notable enhancement in calculation accuracy. The maximum relative error in calculating normal water depth is below 0.067%, and the calculation error for critical water depth does not exceed 0.182%, indicating a broad spectrum of practical applications of the proposed formula. This study introduces a novel approach for determining the characteristic water depth, highlighting the high precision and broad applicability of the proposed formula in non-pressure water conveyance systems, such as tunnels and pipelines