二次抛物线形渠道临界水深与共轭水深简化算法

Simplified Calculation Method of Critical Depth and Conjugate Depth for Second-degree Parabolic Channels

针对目前二次抛物线形断面渠道临界水深与共轭水深计算过程及表达式复杂的问题,推导了抛物线形渠道临界水深的通用直接计算公式,进而推求出二次抛物线形渠道共轭水深的隐性关系式,再采用Matlab仿真平台对抛物线形渠道的共轭水深的高次隐函数方程以实例进行了编程求解。为验证该方法的可靠性与准确性,同时将隐函数方程变形为收敛的迭代公式,通过临界水深选出迭代初值对共轭水深进行迭代求解。对比结果表明,Matlab软件编程法简捷、精确、便于实际应用。

Given the complexity of calculation process and expression form of the critical depth and conjugate depth for parabolic channels,a universal direct calculation formula of critical depth is deduced.And the paper developed the implicit function equation of conjugate depth for parabolic channel is derived.Then,Matlab simulation platform is adopted to program and solve high-order implicit function equation of conjugate depth for an applicative example.To verify the reliability and accuracy of this method,the convergent iterative formula is established from the mathematical deformation of the implicit function equation,and the initial iteration value is selected according to the critical depth value.Finally,the conjugate depth value is found out.The comparison of results proves that Matlab program is simple and exact,and it is very convenient for practical application.