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针对目前计算梯形明渠共轭水深的求解公式存在计算过程复杂、精度低、适用范围小三大弊端,提出一种新的直接计算公式.通过引入一个量纲一参数——单位水面宽度,对梯形明渠共轭水深的水跃方程进行恒等变形,得到了计算梯形明渠共轭水深的迭代公式,再与合理的迭代初值进行配合使用,推导出梯形明渠共轭水深的直接计算公式,误差分析及实例计算表明,在工程常用范围内最大相对误差仅为1.1%.与现有计算公式比较,该直接计算公式形式相对简捷,适用范围广,计算精度高.
A new direct calculation formula is proposed to solve the present calculation formula of conjugate water depth of trapezoidal open channel because of complex calculation process, low precision and small application scope. By introducing a dimension parameter - unit water surface width, The conjugate water depth of the hydrostatic equation is transformed to an equal degree, an iterative formula for calculating the conjugate water depth of the trapezoidal open channel is obtained, and then a reasonable iterative initial value is used in combination to derive the direct calculation formula and error analysis of the conjugate water depth of the trapezoidal open channel. The example calculation shows that the maximum relative error is only 1.1% in the common range of engineering. Compared with the existing calculation formulas, this direct calculation formula has the advantages of relatively simple form, wide application range and high calculation accuracy.