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# Cunge 1980 formula
This flow law corresponds to the equations described by Cunge in his book [^1], or in more detail in an article by Mahmood and Yevjevich [^2]. This law is a compilation of the classical laws taking into account the different flow conditions: submerged, free flow, free surface and in charge as well as the equations [CEM88(D) : Weir / Orifice (important sill)](cem_88_d.md) and [CEM88(D) : Weir / Orifice (low sill)](cem_88_v.md). However, contrary to these equations, it does not provide any continuity between free surface and in charge flow conditions. This can lead to design problems in the vicinity of this transition.
This stage discharge equation is based on the equations described by Cunge in his book [^1], or in more detail in an article by Mahmood and Yevjevich [^2]. This law is a compilation of the classical laws taking into account the different flow conditions: submerged, free flow, free surface and in charge as well as the equations [CEM88(D) : Weir / Orifice (important sill)](cem_88_d.md) and [CEM88(D) : Weir / Orifice (low sill)](cem_88_v.md). However, contrary to these equations, it does not provide any continuity between free surface and in charge flow conditions. This can lead to design problems in the vicinity of this transition.
This law is suitable for a broad-crested rectangular weir, possibly in combination with a valve. The default discharge coefficient \(C_d = 1\) corresponds to the following discharge coefficients for the classical equations:
- \(C_d = 0.385\) for [the free flow weir](seuil_denoye.md).
- \(C_d = 1\) for [the submerged weir](seuil_noye.md).
- \(C_d = 1\) for [the submerged gate](vanne_noyee.md).
- \(C_d = 0.7\) for [the free flow gate](vanne_denoyee.md) but the equation used here is different (see below) especially for an opening \(W\) greater than the critical height.
- \(C_c = 0.611\) for [the free flow gate](vanne_denoyee.md) with \(C_d\) calculated from \(C_c\) (See below).
## Free flow / submerged regime detection
@@ -36,15 +36,15 @@ $$ W \leq Z_2$$
## Discharge equations
The free flow gate equation is slightly different than the classical formulation:
The free flow gate equation uses a fixed contraction coefficient \(C_c\) with:
$$ Q = C_d L W \sqrt{2g} \sqrt{(h_1 - W)}$$
\(C_d = \frac{C_c}{\sqrt{1 + C_c W / h_{am}}}\)
For all other flow regimes, used equations here are the following:
For all other flow regimes, used equations here are the following as they can be used independently:
| | Free surface | In charge |
|--------|---------------|-----------|
| Free flow | [Free flow weir](seuil_denoye.md) | Voir ci-dessus |
| Free flow | [Free flow weir](seuil_denoye.md) | [free flow gate](vanne_denoyee.md) |
| Submerged | [Submerged weir](seuil_noye.md) | [Submerged gate](vanne_noyee.md) |
[^1]: Cunge, Holly, Verwey, 1980, "Practical aspects of computational river hydraulics", Pitman, p. 169 for weirs and p. 266 for gates.