现有底流消能计算中,综合式消力池坎高与池深组合计算的传统试算法十分繁琐,特别是坎上淹没系数计算需多次反复查表试算。为解决这一问题,通过无量纲原理、数学推导及MatLab软件数值分析,给出了坎上淹没系数简洁的高精度解析计算式,并通过对比分析得到该解析计算式最大相对误差仅为0.405%;同时还给出了跃后共轭水深的高精度解析计算式。在考虑消力池深与消力坎的组合消能影响下,给出简洁的无量纲消力坎坎高的解析计算式,并通过MatLab软件给出了无量纲坎高随无量纲单宽流量、下游水深以及消力池池深之间的二维曲面关系图,依据大量数值计算成果,给出了最不利消能工况下的坎高极值计算式。最后通过2个实例计算对比,可见所提出的简洁算法精度高且方便快捷,为工程实际设计提供了参考。

Traditional trial calculation method for the sill height and depth of stilling pool for energy dissipation is burdensome, and in particular, the calculation of submergence coefficient requires repeated check. In view of this, in the light of dimensionless principle, a simple analytical solution to submergence coefficient is given through mathematical deduction and numerical analysis in MatLab. The solution is of high precision with the maximum relative error only 0.405%, favorable for engineering application. Moreover, the analytical formula of conjugate water depth after jump with dimensionless unit width discharge parameter λ is given, and a concise analytical formula of dimensionless sill height is also presented. In addition, the two-dimensional surface diagram of dimensionless sill height with dimensionless unit width discharge, downstream water depth, and stilling pool’s depth are obtained. The calculation formula for the extreme value of sill height under the most unfavorable energy dissipation condition is also given. The depth of stilling pool and sill height displays an approximate negative linear relation, which is affected by submergence coefficient and dimensionless parameter K. Two engineering calculation examples verify that the formulas proposed in this paper are highly precise and convenient.