半立方抛物线形渠道正常水深算法

为了给半立方抛物线形渠道断面正常水深的计算提供一种简捷、通用、精度较高的显函数计算公式,根据迭代理论并采用优化计算确定初值函数的方法进行分析研究.通过引入断面特征水深的概念,对半立方抛物线形渠道正常水深的基本方程进行变换处理,推导出收敛速度较快的迭代公式,并证明了公式的收敛性;在断面特征水深范围即无量纲正常水深H∈[0.025,40]范围内,对迭代公式进行优化计算,取得合理的迭代初值函数;合理初值与迭代公式的配合使用,得到半立方抛物线形渠道断面正常水深的显函数直接计算公式,并对公式进行了误差分析以及用工程实例进行了验证.结果表明：在工程常用的断面特征水深范围内,正常水深的最大相对误差小于0.3%,计算公式具有形式简单、精度高、适用范围广的优点,该研究为排灌渠道的断面设计以及渠道流量控制时求解均匀流水深提供了简捷方法.

Calculation method for normal depth of semi-cubic parabolic channels

 In order to obtain the simple and general explicit formula with high accuracy for computing the normal depth of semi-cubic parabolic channels,formula for direct computation of the normal depth was developed by obtaining initial function using iteration theory and optimization.Mathematical transformation on the basic equation for determining the normal depth of semi-cubic parabolic channel was made by introducing the concept of characteristic depth of cross-section,and the iterative formula with high convergence rate was derived.According to the optimization of the iterative formula in the range of 0.025 to 40 for dimensionless normal depth H,the reasonable initial function was developed.Direct calculation formula for computing the normal depth of semi-cubic parabolic channels was obtained by using the reasonable initial value and iterative formula.Error analysis of the formula was also carried out.The result indicates that the maximum relative error of the formula is less than 0.3% for the most frequently used range of characteristic depth of cross-section.The formula developed in this paper is simple and has high accuracy with wide range of applications,and it can provide simple method for computing the normal depth when the channel section is designed for irrigation and drainage and controlling the water level