中文摘要：

考虑底坡影响的条件下,利用均值不等式对明渠恒定非均匀流最小断面比能和临界水深的计算公式进行改进,并附以算例验证。通过对改进前后两种方法的比较,结果表明：采用改进后的计算方法较之传统计算方法得到的临界水深偏大,最小断面比能偏小。改进后的公式利用均值不等式理论简化了计算过程,且考虑底坡影响下的结果更为精确,可靠度更高。这一改进过程从理论上阐述了数学方法在水力学分析中应用的可行性,同时也为水力学课程教学与工程实际计算提供了新的指导思路和简便的解决途径。

英文摘要：

Under the consideration of the influence from bottom slope, the formula for calculation of the minimum specific energy of the steady non-uniform flow and the critical water depth in open channel is modified with the mean inequality; moreover, it is verified with the attached calculation case. Through the comparison made between both the methods before and after the modifica- tion, the result shows that obtained from the modified method, the critical water depth is a little bit larger and the minimum spe- cific energy is a little bit smaller than those got from the conventional one. The calculation process is simplified by the modified formula with the theory of the mean inequality, from which the results under the consideration of the influence of bottom slope are more accurate with high reliabilities. This modified process theoretically describes the feasibility of the application of mathematical method to hydraulic analysis, meanwhile it provides a new guiding idea and simple solution way for the teaching of hydraulics and the actual engineering calculation concerned as well.