矩形断面收缩水深的简化计算法

针对目前矩形断面收缩水深计算方法存在的计算繁复、结果精度不高等问题,经过对矩形断面收缩水深基本方程的进一步整理,引入幂级数展开并经适当简化,获得了形式较为简单的迭代初值函数,经一次迭代后通过数学方法推求出了表达形式简单、容易记忆、计算简捷、便于实际应用、成果精度可靠的近似计算公式,通过精度分析及计算举例表明,在工程实用范围内(即0<α≤0.4,α为无量纲水深),计算相对误差小于0.54%,具有较好的应用推广价值。

Simplified Calculation Method for Contracted Water Depth of Rectangular Cross-section

According to the complicated calculation and low accuracy of fruits in the contracted water depth calculation of rectangular cross-section,and after sorting out the basic equations for the calculation,the power series is introduced and simplified to get the relatively simple iteration early-value function.Then after the first iteration,the approximate calculation formula is deduced by the mathematical method,which is simple,easy to remember and compute,convenient for practical application,and reliable in the result’s accuracy.The analysis and application results show that in the range of practical engineering(ie,0<α≤0.4,α as dimensionless water depth),the relative error of the calculation is less than 0.54%,which has a good application value.