Free weir formula
The formula is derived from the original formula of Poleni (1717).
In a free flow, the flow rate depends only on the upstream water level \(h_{amont}\):
\[Q = Cd \sqrt{2g} L h_{amont}^{3/2}\]
With:
- Q the flow in m3/s
- Cd the discharge coefficient
- \(g\) the acceleration of gravity 9.81 m/s2
- L the width of the weir in m
- hamont the upstream water level above the crest of the weir in m
A flow coefficient value \(C_d = 0.4\) is generally a good approximation for a rectangular weir. For more complex weir shapes (trapezoidal, circular...) or to take into account the characteristics of the longitudinal profile (thin-crested weir, thick-crested weir), one can refer to the CETMEF weir leaflet (CETMEF, 2005).