平底矩形渐扩挖深式消力池深度计算新公式

为解决平底矩形渐扩挖深式消力池深度计算传统公式与等宽矩形断面消力池深度计算公式不统一的问题，通过建立收缩断面水深方程、水跃方程、出池落差方程和消力池末端几何关系方程推导了渐扩矩形断面挖深式消力池深度计算的新公式。分析认为，传统公式计算消力池深度存在小于新公式计算结果的情况，以传统公式计算的消力池深度作为设计依据不能完全形成确定淹没系数的淹没水跃，此时下游河床冲刷较大，无法满足消能的设计要求；当消力池首、末宽度相等时，新公式与等宽矩形断面消力池深度计算公式相同，且新公式物理概念清晰，以新公式计算的消力池深度作为工程设计的依据更加可靠。

New formula for calculating the depth of a rectangular expanding deep excavation energy dissipation basin with a flat bottom

To address the inconsistency between the traditional formula for calculating the depth of a flat-bottom rectangular expanding deep excavation energy dissipation basin and the formula for calculating the depth of an equal-width rectangular section energy dissipation basin, a new formula for calculating the depth of an expanding rectangular section deep excavation energy dissipation basin has been derived. This derivation involves establishing equations for the contraction section water depth, hydraulic jump, basin outflow drop, and the geometric relationship at the end of the energy dissipation basin. Analysis suggests that the traditional formula for calculating the depth of the energy dissipation basin often yields results smaller than those obtained using the new formula. Using the depth calculated by the traditional formula as a design basis may not fully ensure the formation of a submerged hydraulic jump with a determined submergence coefficient. This could lead to significant downstream riverbed erosion and fail to meet energy dissipation design requirements. When the widths at the beginning and end of the energy dissipation basin are equal, the new formula coincides with the formula for calculating the depth of an equal-width rectangular section energy dissipation basin. The new formula, with its clear physical concept, provides a more reliable basis for engineering design.