# Discharge equations at devices

• "CEM 88(V)" (weir-undershoot gate) is the default equation for rectangular or circular gates. It takes into account the different flow conditions (submerged, freeflow, open channel flow, and flow in pressure). Moreover, it assures discharge continuity between these differents flow conditions.
• "CEM 88(D)" (weir-orifice) is default equation for rectangular sill. As "CEM 88(V)" it takes into account all flow conditions with discharge continuity.
• "CUN 80" are equations described by Cunge in his book [1], or in more detail in Mahmood and Yevjevich article [2]. "Cun80"’s equations also take into consideration the different flow conditions: submerged, freeflow, open channel flow, and flow in pressure pipes (as Cemagref equations "CEM 88"), but there is no continuity between conditions of open channel flow and pressure pipes flow. Therefore calculation problems can arise close to this transition.
• "Submerged" equation corresponds to the classical submerged gate equation.
• "Freeflow" equation corresponds to the classical freeflow weir equation.
• "GOU 93 Amil" et "GOU 93 Avi" are the equation proposed by default for GEC-Alsthom AVIS/AVIO and AMIL gates. The latter come from constructor documents and permit to reproduice the characteristics observed in GEC-Alsthom constructor’s abacus.
• "CEM 02(V)" is default equation for trapezoidal gates. It is the sum of "CEM 88(V)" equation for the rectangular part and Gourley equation for the triangular part.
• "CEM 02(V)" is default equation for trapezoidal sills. It is the sum of "CEM 88(D)" equation for the rectangular part and Gourley equation for the triangular part.

[1Cunge, Holly, Verwey, 1980, "Practical aspects of computational to river hydraulics", Pitman, p. 169 for weir and p. 266 for gates

[2Mahmood K., Yevjevich V., 1975, "Unsteady flow in open channels, Volume 1 and 2", Water resources publications, Strong Collins, USA, 923 p