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The Saint-Venant equations, the characteristic system of equations and the simple wave approximation are essential concepts for the numerical modelling of unsteady open channel flows and its practical applications, incl. flood modelling. These are discussed in the relevant Youtube video movies in the same Youtube channel at: { / @hubert_chanson }. Fluid mechanics and hydraulics in Hubert Chanson Youtube channel { / @hubert_chanson } Advanced hydraulics of open channel flows [Playlist] Fundamentals of open channel hydraulics [Playlist] Environmental hydraulics of open channel flows [Playlist] Saint-Venant equations. (1) Presentation { • Saint-Venant equations. (1) Presentation } Saint-Venant equations. (2) Basic equations { • Saint-Venant equations. (2) Basic equations } Saint-Venant equations. (3) The continuity equation { • Saint-Venant equations. (3) The continuity... } Saint-Venant equations. (4) The dynamic equation { • Saint-Venant equations. (4) The dynamic eq... } Saint-Venant equations. (5) Simplification of the dynamic equation { • Saint-Venant equations. (5) Simplification... } Celerity of small wave and its propagation in open channel { • Celerity of small wave and its propagation... } Acknowledgements Dr Jean CUNGE Professor Colin APELT 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). BARRÉ de SAINT-VENANT, A.J.C. (1871). "Théorie et Equations Générales du Mouvement Non Permanent des Eaux Courantes." Comptes Rendus des séances de l'Académie des Sciences, Paris, France, Séance 17 July 1871, Vol. 73, pp. 147-154. STOKER, J.J. (1957). "Water Waves. The mathematical Theory with Applications." Interscience Publishers, New York, USA, 567 pages. LIGGETT, J.A. (1994). "Fluid Mechanics." McGraw-Hill, New York, USA. CHANSON, H. (2004a). "The Hydraulics of Open Channel Flow: An Introduction." Butterworth-Heinemann, 2nd edition, Oxford, UK, 630 pages (ISBN 978 0 7506 5978 9). CHANSON, H. (2004b). "Environmental Hydraulics of Open Channel Flows." Elsevier-Butterworth-Heinemann, Oxford, UK, 483 pages (ISBN 978 0 7506 6165 2).