基于牛顿迭代法的圆形断面临界水深直接计算法  

Direct Formula Calculating Critical Depth of Circular Flow Section

作　　者：邹武停[1] 辛全才[1] 张宽地[1] 

机构地区：[1]西北农林科技大学水利与建筑工程学院,陕西杨凌712100

出　　处：《水电能源科学》2012年第3期100-102,共3页Water Resources and Power

基　　金：国家自然科学基金资助项目(41001159);国家973计划课题基金资助项目(2007CB407201)

摘　　要：通过对圆形断面临界流公式的数学变换,得到其临界水深的牛顿迭代公式,应用最优一致逼近法得到了临界水深中心角θ的近似计算式,并以此近似算式为初值函数,代入迭代方程获得了圆形断面临界水深的直接计算公式。实例计算及误差分析结果表明,在工程实用范围内该方法最大相对误差为0.03%,若用该近似结果再迭代一次,精度则高出104倍。A Newton iterative formula for calculation critical depth of circular flow section is derived through mathe matical transformation from the basic equation. Meanwhile, optimum uniform approximation method is used to obtained approximate formula for calculating central angle 0 at critical depth. Taking the formula as an initial function, it is substi tuted into the iteration function and the direct formula for calculating critical depth of circular flow section is obtained. Calculation illustration and error analysis of the new formula show that the maximum relative error in engineering prac- tices fell within 0. 03%, and the results could even exceeds 104 times if one more iteration is implemented.

关 键 词：圆形过水断面 水力计算 临界水深 牛顿迭代法 

分 类 号：TV131.4[水利工程—水力学及河流动力学]