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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。
Aiming at the commonly used gate-shaped and horseshoe-shaped cross-over tunnels in water conservancy projects, the formula of section parameters Z and hydraulic index M designed for critical flow analysis is given by using the critical flow equation, and the formula for calculating the relationship between water depth and Z and M The relationship curve. The calculated curves show that the M values change very little when the water depth ratio is less than 1.4, if the height and width of the tunnel are equal, and approximate critical flow characteristics when the water depth ratio reaches 1.90. The analysis and calculation also show that it is impossible for the dome tunnel to reach the critical flow state when the water depth is infinitely close to the top of the tunnel. However, when the water level in the tunnel is high, the wave surface of the critical flow can cause the cap flow earlier. The formulas and curves provided can be referenced to the hydraulic design of the tunnel.