Froude number and open channel flow

The Froude number is a dimensionless number defined as the ratio of a characteristic velocity scale V to the square root of the gravity acceleration g times a characteristic length scale L. The dimensionless number is commonly used in open channel flows.
In open channel flows, the Froude number may be derived from different fundamental principles:
-Dimensional considerations and the application of the Pi-Buckingham theorem to free-surface flows because the gravity effects are important.
-The dimensionless number may also be derived based upon energy considerations and the backwater equation.
-The Froude number may be derived as well as from momentum considerations, e.g. the Bélanger equation for a hydraulic jump.
-A further consideration is the dimensionless specific energy and critical flow conditions at minimum specific energy.
The concepts of Froude number, critical flow conditions, hydraulic jump and backwater equation are essential to the understanding of open channel hydraulics. These are discussed in the relevant Youtube video movies in the same Playlist at: {   / @hubert_chanson  }.

Applied Hydrodynamics in Hubert Chanson Youtube channel {   / @hubert_chanson  }
Fundamentals of open channel hydraulics [Playlist]
Advanced hydraulics of open channel flow [Playlist]

Critical flow conditions in open channels {https://www.youtube.com/watch?v=8mk‐l...}
Subcritical and supercritical flow in open channel {   • Subcritical and supercritical flow in open...  }
Celerity of small wave and its propagation in open channel {   • Celerity of small wave and its propagation...  }
On the analogy between Mach and Froude numbers {   • On the analogy between Mach and Froude num...  }
Physical modelling in hydraulic engineering (4) Froude similitude {   • Physical modelling in hydraulic engineerin...  }

References
BAKHMETEFF, B.A. (1912). "O Neravnomernom Dwijenii Jidkosti v Otkrytom Rusle." St Petersburg, Russia (in Russian).
BELANGER, J.B. (1828). "Essai sur la Solution Numérique de quelques Problèmes Relatifs au Mouvement Permanent des Eaux Courantes." Carilian-Goeury, Paris, France, 38 pages & 5 tables (in French).
BÉLANGER, J.B. (1841). "Notes sur l'Hydraulique." ('Notes on Hydraulic Engineering.') Ecole Royale des Ponts et Chaussées, Paris, France, session 1841-1842, 223 pages (in French).
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).
CHANSON, H. (2009). "Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)." Journal of Hydraulic Engineering, ASCE, Vol. 135, No. 3, pp. 159-163 (DOI: 10.1061/(ASCE)0733-9429(2009)135:3(159))
CHANSON, H. (2012). "Momentum Considerations in Hydraulic Jumps and Bores." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 138, No. 4, pp. 382-385 (DOI 10.1061/(ASCE)IR.1943-4774.0000409).
CHANSON, H. (2014). "Applied Hydrodynamics: An Introduction." CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 448 pages & 21 video movies (ISBN 978-1-138-00093-3).