突然扩散水跃方程的近似解

An approximate solution of the hydraulic jump equation in abruptly expanding channel

突然对称扩散水跃被广泛地应用于实际工程。本文研究了突然扩散水跃方程及它的近似解特性,应用动量守恒原理推导了突然扩散水跃共轭水深关系式。通过级数展开处理,获得了突然扩散水跃方程的近似解,给出了确定有关参数的经验公式。不同突扩比时突然扩散水跃方程的近似解与实验结果的平均误差为5.642%,可见与实验结果吻合较好。另外,将近似解应用到矩形渠槽的水跃,结果说明与实验的平均误差为1.943%。在稳定水跃范围内,与矩形明渠水跃典型理论解的最大误差为1.2%。近似解能很好地与理论解及实验一致,这说明水跃方程近似解具有较高的精度,是可靠的。本文近似解可以应用到计算工程问题。

Hydraulic jump in abruptly expanding channel is widely used in practical engineering.In this paper,hydraulic jump equation in abruptly expanding channel and its approximate solution characteristics are studied.The equation of conjugate water depth of hydraulic jump in abruptly expanding channel is derived by momentum conservation principle.By means of series expansion,the approximate solutions of the hydraulic jump equation in abruptly expanding channel are obtained,and the empirical formula for determining the parameters is given.The average error between the approximate solutions and the experimental results of the abrupt expansion hydraulic jump equation for different abrupt expansion ratios is 5.642%.Therefore,the approximate solutions are in good agreement with the experimental results.In addition,applying the approximate solutions to the hydraulic jump in a rectangular open channel,the results show that the average error between the approximate solutions and the experiment is 1.943%,and the maximum error of the approximate solution relative to the classically theoretical solution in a rectangular open channel is 1.2%in the range of a steady jump.Obviously,the approximate solutions are in good agreement with the theoretical solutions and the experiments.It shows that the approximate solutions of the hydraulic jump equation have high accuracy and are reliable.The approximate solutions are applicable to the hydraulic calculation in hydraulic engineering.