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城门洞形断面是输水隧洞工程中一种经常采用的过水断面形式。其临界水深方程是含未知参数的超越方程 ,数学上无解析解。常见计算方法有图解法或迭代试算法。这些方法都繁琐复杂 ,而且图解法误差大 ,还依赖图表 ,不便应用。为满足生产实践之急需 ,通过对其临界流基本方程的数学变换 ,并应用优化拟合原理 ,给出其近似解析解 ,从而提出一种近似计算公式。结果表明 :在实用范围内 (临界水深度与拱顶半径之比在 1.1到 1.8之间 ) ,临界水深度的最大误差不超过 0 .5 %。该法比现行的查图查表法、迭代试算法更简捷、更精确
Shing Mun tunnel-shaped cross-section of the water tunnel project is often used in the form of cross-section. The critical water depth equation is the transcendental equation with unknown parameters, and there is no analytic solution in mathematics. Common methods of calculation are graphical or iterative test method. These methods are cumbersome and complex, and graphically large error, but also dependent on the chart, inconvenient to use. In order to meet the urgency of production practice, an approximate calculation formula is proposed by mathematical transformation of the basic equations of its critical flow and application of the principle of optimal fitting. The results show that within practical limits (the ratio of critical water depth to dome radius is between 1.1 and 1.8), the maximum error of critical water depth does not exceed 0.5%. This method is more concise and accurate than the current look-up table method and iterative test method