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| Name | Celerity of small wave and its propagation in open channel |
| Video Uploader | Video From Hubert Chanson |
| Upload Date | This Video Uploaded At 04-01-2022 22:00:18 |
| Video Discription | Let us consider a small wave propagating in a horizontal channel initially at rest. For an observer travelling with the wave, the continuity and energy equations may be written between an upstream location and the cross-section where the wave height is maximum. For an infinitely small disturbance, the previous result yields the celerity C of a small disturbance in an open channel, first derived by Joseph-Louis Lagrange (1781): C = sqrt(g.d) in a rectangular channel. The Froude number may be written in a form analogous to the Sarrau-Mach number in compressible flow, as the ratio of the flow velocity divided by the celerity of small disturbances. The study of two-dimensional supercritical flow in open channel is very similar to the study of supersonic gas flow. The analogy was applied with some success during the early laboratory studies of supersonic flows. At the beginning of high-speed aerodynamics (i.e. late 19th century and first half of the 20th century), the propagation of oblique shock waves in supersonic (compressible) flows was deduced from the propagation of oblique shock waves at the free surface of supercritical open channel flows. Interestingly the celerity C of a small disturbance in open channel flow is slow compared to the sound celerity and it can be easily observed. Fluid mechanics ad hydraulics in Hubert Chanson Youtube channel {https://www.youtube.com/channel/UCm-SedWAjKdQdGWNbCwppqw} Fundamentals of open channel hydraulics [Playlist] Advanced hydraulics of open channel flows [Playlist] Applied Hydrodynamics [Playlist] Joseph-Louis Lagrange Critical flow conditions in open channels Hydraulic control in open channels: upstream and downstream controls Acknowledgements NASA References LAGRANGE, J.L. (1781). "Mémoire sur la Théorie du Mouvement des Fluides." ('Memoir on the Theory of Fluid Motion.') in Oeuvres de Lagrange, Gauthier-Villars, Paris, France (printed in 1882) (in French). LIGGETT, J.A. (1994). "Fluid Mechanics." McGraw-Hill, New York, USA. 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. (2014). "Applied Hydrodynamics: An Introduction." CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 448 pages & 21 video movies (ISBN 978-1-138-00093-3). CASTRO-ORGAZ, O., and CHANSON, H. (2022). "Free surface profiles of near-critical instabilities in open channel flows: undular hydraulic jumps." Environmental Fluid Mechanics (DOI: 10.1007/s10652-021-09797-3). |
| Category | Science & Technology |
| Tags | hydraulic structures | turbulence | environmental fluid mechanics | hydraulic engineering | Small waves | Small disturbances | Shock waves | Froude number | Mach number | Supersonic flow | Supercritical flow | Open channel flows | Surface wave |
