城门洞形及马蹄形过水隧洞的临界水流

针对水利工程上常用的城门洞形及马蹄形过水隧洞，利用临界流方程，给出了旨在用于临界流分析的断面参数Ｚ和水力指数Ｍ 的计算公式和表示水深与Ｚ以及Ｍ 之间的关系曲线。计算曲线表明，若隧洞的高宽相等，在水深比小于１．４ 时， Ｍ 值的变化范围很小，而当水深比达到１．９０时，两种隧洞具有近似的临界流特征。分析和计算还表明，圆顶隧洞在水深无限接近洞顶时不可能出现临界流状态，但洞内水位较高时，其临界流的波状水面可较早地引起封顶水流。所提供的公式和曲线可为隧洞的水力设计所参考。

Critical flow in city-gate and horseshoe conduit

Based on the basic critical flow equation, formulae, which used to determine section factor Z and hydraulic exponent M for critical flow in city gate and horseshoe conduits, were derived. Dimensionless curves showing the relation between the depth and Z , the depth and M , have been prepared to simplify the analysis and computation of critical flow. When the value of y/r was greater than 1.9, the curves showed that both conduits have approximately the same critical depth or discharge. In addition, the value of M varied within a rather narrow range for values of y/r less than 1.4. Theoretically it is impossible to maintain a critical flow in city gate and horseshoe conduit if the water surface approaches to the top of the circle. It should be noticed, however, that critical flow can still happen in them and that the wavy surface of it can touch the top of the tunnel if the water depth is higher.