悬链线形断面渠道临界水深的简化计算

Simplified Calculation for Critical Depth of Catenary Canal

悬链线形断面渠道临界水深计算涉及超越方程求解,用解析法不能直接获解。由于传统解法(试算法及图表法)计算过程繁琐且精度不易保证,利用计算机求解又需编程不便实际应用。为了获得简便实用的计算方法,经对该种断面临界水深计算公式的变形整理,通过引入无量纲水深参数,采用优化拟合的方法,以标准剩余差最小为目标函数,在工程适用参数范围内,经逐次逼近拟合计算获得了表达形式简单、求解成果精度高的近似计算公式(最大拟合相对误差仅为0.515%),具有一定的实用意义。

The calculation for the critical depth of catenary canal involves the transcendental equation, so the analytical method can not be directly used for the solution. The calculation process of traditional methods（test algorithm and chart method） is tedious and not easy to ensure accuracy, and using computer for solution needs programming, which is incon- renient in practical application. In order to obtain the simple and practical method of calculating, the deformation and sorting are carried out for the critical depth formulas of this kind of cross-section by introducing the dimensionless water depth parameter. Then, through the optimization fitting method, taking the minimum remaining difference as the objec- tive function, and within the range of the applicable parameters in engineering, the expression is obtained by successive approximation fitting calculation, which is simple and precise（maximum relative error of only 0. 515 % ）. This approxi- mate formula has some practical significance.