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半立方抛物线形断面渠道收缩水深的计算较困难,主要是因为需要求解高次隐函数,传统的图解法和试算法计算结果精度较低,且过程复杂,不方便应用到实际工程中。该文通过合理变形处理半立方抛物线形断面渠道收缩水深的基本方程,得到迭代公式,并证明了其收敛性,再通过求解方程获得迭代初值函数,进而得到半立方抛物线形渠道断面的收缩水深公式,经误差分析,在实际工程常用范围内,收缩水深初值最大相对误差小于0.27%,经一次迭代后,收缩水深最大相对误差小于0.06%。实际算例表明,该计算公式形式简单,计算结果精度高,适用范围广。
The calculation of the shrinkage depth of the semi-cubic parabolic cross-section channel is difficult because it is necessary to solve the implicit function of high order. The accuracy of the traditional graphical method and the trial method is low, and the process is complex and inconvenient to apply to practical projects. In this paper, by iteratively dealing with the basic equations of water depth of the semi-cubic parabolic cross-section, the iterative formula is obtained, and its convergence is proved. Then the iterative initial value function is obtained by solving the equation and the shrinkage depth of the semi-cubic parabolic channel is obtained Formula, the error analysis shows that the maximum relative error of the initial value of shrinkage depth is less than 0.27% in the common range of practical engineering. After one iteration, the maximum relative error of shrinkage depth is less than 0.06%. The actual example shows that the formula is simple in form, high precision and wide range of application.