梯形明渠共轭水深计算方法

Calculation Method for Conjugate Water Depth in Open Trapezoidal Channel

一方面,通过对共轭水深方程进行数学变换,并根据共轭水深的水流特点,得到计算其水深的迭代公式;另一方面,通过求解一元二、三次方程得到共轭水深的初值近似计算式,并以此为初值,用迭代公式进行一次迭代得到梯形明渠共轭水深的直接计算公式。计算数据表明,该法不依赖图表,计算便捷且精度很高,可供工程实际参考应用。

A calculation method for the conjugate water depth in open trapezoidal channel is presented.First of all,an iterative formula for the conjugate depth is given on the basis of mathematical transformation of the basic equation of conjugate depth and its flow characteristics.Subsequently,by solving unary quadratic equation and cubic equation,an approximate formula for the initial value of conjugate water depth is obtained,based on which an expression for the initial value iteration is established.A direct formula is thus obtained by using the iterative formula.An illustrative calculation indicates that this method is simple and accurate,and the neither table nor figure is needed to determine the empirical coefficients.