无压流圆形断面收缩水深的近似计算公式

An Approximate Calculation Formula of Contracted Water Depth in Free Flow Circular Cross-section

无压流圆形断面收缩水深的计算需求解高次隐函数方程,理论上无解析解,传统的图解法或者试算法计算过程复杂,费时费力.通过引入无量纲收缩水深,对无压流圆形断面收缩水深的基本方程进行恒等变形,得到了快速收敛的迭代公式,再与合理的迭代初值配合使用,得到无压流圆形断面收缩水深的近似计算公式.误差分析及实例计算表明,在工程常用范围内,收缩水深的最大相对误差小于0.72%.近似计算公式形式简捷、精度高、适用范围广.

The contracted water depth in circular cross-section needs to solve the high implicit function equation. There is no analytical solution theoretically. The graphical method or test algorithm is complicated and time and effort consuming. This thesis obtains the iterative formula with the rapid convergence by constant deformation on the basic equation of the contracted water depth in circular cross-section; further it can obtains the approximate calculating formula of contracted water depth in circular cross-section with the reasonable initial iteration. The error analysis and examples manifest that the maximum relative error of contracted water depth is less than 0.72% within the common project. The formula has a direct and simple form, high precision and wide application.