三种抛物线形渠道共轭水深的显式计算公式

摘要

In order to get the explicit calculation formula of conjugate depth for semi-cubic,square,and cubic para-bolic-shaped channels,the jump equations of the three parabola-shaped channels were transformed identically and the relationships between the dimensionless water depth x before jump and the dimensionless water depth y after jump were obtained according to the property that the critical depth was between the pre-jump depth and the post-jump depth.Their iterative formulas were further obtained respectively.Hence,a set of explicit calculation formu-las of conjugate depth for semi-cubic,square,and cubic parabolic-shaped channels were obtained by fitting the it-erative initial value through excel in common engineering scope.Finally,example and error analysis shows that the absolute value of maximum relative error of dimensionless water depth x before jump was 0.25%,0.1 7%,and 0.31 % respectively for the semi-cubic,square,and cubic parabolic-shaped channel,and that of dimensionless wa-ter depth y after jump was respectively -0.23%, -0.29%,and 0.39%.The formulas were convenient and highly accurate with clear physical meaning and wide application scope.%为了得到半立方、平方、立方抛物线形渠道共轭水深的显式计算公式，对这3种抛物线形渠道的水跃方程进行恒等变形，利用临界水深介于跃前水深和跃后水深之间的性质，得到了无量纲跃前水深 x 和无量纲跃后水深 y之间的关系式，进一步分别得到其迭代公式。在工程常用范围内，利用 excel 拟合得到其迭代初值，提出了一套抛物线类渠道共轭水深的显式计算公式。最后，实例及误差分析表明：半立方、平方、立方抛物线形断面无量纲跃前水深 x、无量纲跃后水深 y 最大相对误差分别为0．25％，－0．23％；0．17％，－0．29％；0．31％，0．39％。公式物理概念清晰，计算简捷，精度高，适用范围广。