Fluid Mechanics - When will a hinged gate tip?

This video movie discusses a basic fluid mechanics application: a hinged gate and when will it tip? We review how to solve the problem. First, we need a good sketch, with the correct boundary conditions, and relevant symbols. Second, let us consider what is causing the gap to tip? and what is preventing the gate to tip? The key driver is the hydrostatic pressure in the reservoir and the hydrostatic pressure distribution on the gate. a complete solution is derived based upon angular momentum. The results demonstrate that the hinged gate cannot tip when the hinge is located above 21% of the gate height. At lower hinge locations, tipping is a function of the relative water depth in the reservoir and hinge location.
Relevant practical applications include control structures in urban water supply systems, bottom outlets at dams and reservoirs, sewers and tidal gates
For completeness, this problem was first proposed in an engineering fluid mechanics textbook - which is not named, under conditions - that were physically meaningless.
References and bibliography
ROUSE, H. (1938). "Fluid Mechanics for Hydraulic Engineers." McGraw-Hill Publ., New York, USA (also Dover Publ., New York, USA, 1961, 422 pages)
HENDERSON, F.M. (1966). "Open Channel Flow." MacMillan Company, New York, USA.
HAMILL, L. (1995). "Understanding Hydraulics." MacMillan, London, UK.
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).
Hubert CHANSON KZbin channel { / @hubert_chanson }
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