Application of the energy equation to a siphon spillway

A siphon is a pipe connecting two reservoirs of different water levels, in which the pipe pressure would locally become less than atmospheric. In the siphon, the liquid flows from the upper reservoir to the lower reservoir, and the driving process is gravity. In the first part, the siphon lifts the liquid up to an elevation higher than the surface of the upper reservoir, until a maximum elevation where the pressure is sub-atmospheric, before discharging into the lower reservoir. An application is the siphon spillway. This photograph shows a physical model of siphon spillway.
Now, let us consider a simple application of the energy principle to a siphon spillway. A 25 m high concrete gravity dam is equipped with a siphon spillway system. The siphon spillway was primed during a flood event and is operating under pressure flow. The 19 m long siphon has a constant cross-section of 2 m × 1 m. The friction factor f is 0.022, the inlet loss coefficient is 0.5, the bend loss coefficient at the crown is 0.75, and the outlet loss coefficient is 1.0.
● Calculate the discharge when the reservoir surface elevation difference is 7.5 m.
● Determine the pressure at the crown (Point C), located 6.5 m from the inlet for the flow conditions shown below.
Note that the schematic below shows flow conditions corresponding to the tail of the flood, once the upstream reservoir elevation has considerably lowered.
The operation of siphon spillways constitutes a basic application of fluid mechanics and energy principle to open channel hydraulics and hydraulic structures. This is further discussed in a number of relevant RUclips video movies in the same channel at: { / @hubert_chanson }
 
Hydraulic Engineering and Applied Hydrodynamics in Hubert Chanson RUclips channel { / @hubert_chanson }
Fundamentals of open channel hydraulics [Playlist]
Advanced hydraulics of open channel flow [Playlist]
Hydraulic structures [Playlist]
The Equation of Conservation of Mass in Fluid Mechanics { • The Equation of Conser... }
Equation of conservation of energy in fluid mechanics { • Equation of conservati... }
The siphon { • The siphon }
The inverted siphon { • The inverted siphon }
The air-regulated siphon { • The air-regulated siphon }
Acknowledgements
Late Prof. Alan ERVINE
References
ERVINE, D.A., and OLIVER, G.C.S. (1980). "The full-scale behaviour of air-regulated siphon spillways." Proceedings of the Institution Civil Engineers, Part 2, Vol. 69, pp. 687-706.
CHANSON, H. (2004). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9).
NOVAK, P., MOFFAT, A.I.B., NALLURI, C., and NARAYANAN, R. (2007). "Hydraulic Structures." Taylor & Francis, London, UK, 4th edition, 700 pages.