针对现有高坝消力戽消能计算十分繁琐的问题,考虑底挑圆弧离心力对收缩水深的影响,基于无量纲化理论、水力学基本理论和数学理论推导,给出了高坝消力戽消能计算基本方程。利用一元三次方程的卡当公式解分别给出了坎底收缩水深和跃后共轭水深的解析计算公式,并采用MatLab计算软件对跃后共轭水深与无量纲单宽流量、无量纲总水头以及消力戽底坎挑角的影响关系进行了计算研究。最后通过工程实例计算比较,认为推导的坎底收缩水深和跃后共轭水深计算式精度可靠,方便快捷,便于工程实际应用。

In view that the calculation of energy dissipation bucket for high dam is very complicated, the influence of centrifugal force of bottom arc on the contraction of water depth is considered in giving basic equations of energy dissipation based on the theory of dimensionlessness, the basic theory of hydraulics and the derivation of mathematical theory. Equations of the contracted water depth at the bottom of bucket and the downstream conjugate water depth are given respectively by using the Cardan formula of simple cubic equation. Moreover, MatLab software is used to calculate the relationship among conjugate water depth and dimensionless discharge per unit width, dimensionless total head and bucket angle. Calculation and comparison on engineering examples proves that the proposed equations for bottom contracted water depth and downstream conjugate depth are accurate, reliable and convenient to be applied to practical project.