I need the English version of this paper which was publish in 1871.
The US Army Corps of Engineers Library has an English translation.
http://acwc.sdp.sirsi.net/client/en_US/default/search/detailnonmodal/ent:$002f$002fSD_ILS$002f0$002fSD_ILS:58141/ada/?rt=CKEY|||CKEY|||false
You may find a more modern and rigorous derivation in the paper described below, available on my ResearchGate account. The reference list contains pointers to several other attempts to derive the same equations while taking into account terms that are usually discarded in standard derivations.
Best regards
Luca Bonaventura
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Asymptotic derivation of the section-averaged shallow water equations for natural river hydraulics
Astrid Decoene · Luca Bonaventura · Edie Miglio · Fausto Saleri
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ABSTRACT: The section-averaged shallow water model usually applied in river and open channel hydraulics is derived asymptotically up to second order in the vertical/longitudinal length ratio, starting from the three-dimensional Reynolds-averaged Navier-Stokes equations for incompressible free surface flows. The derivation is carried out under quite general assumptions on the geometry of the channel, thus allowing for the application of the resulting equations to natural rivers with arbitrarily shaped cross sections. As a result of the derivation, a generalized friction term is obtained, that does not rely on local uniformity assumptions and that can be computed directly from three-dimensional turbulence models, without need for local uniformity assumptions. The modified equations including the novel friction term are compared to the classical Saint Venant equations in the case of steady state open channel flows, where analytic solutions are available, showing that the solutions resulting from the modified equation set are much closer to the three-dimensional solutions than those of the classical equation set. Furthermore, it is shown that the proposed formulation yields results that are very similar to those obtained with empirical friction closures widely applied in computational hydraulics. The generalized friction term derived therefore justifies a posteriori these empirical closures, while allowing to avoid the assumptions on local flow uniformity on which these closures rely.
Mathematical Models and Methods in Applied Sciences 03/2009; 19(3). DOI:10.1142/S0218202509003474
@all. Thanks for all the links.
@Jeffrey, there isn't a link to directly download the paper. I had to message the librarian.
@Luca, thanks for your contributions. Your paper really has direct connection to our own ideas but with a bit different approache. I just wanted the original St Venant paper to see the actual discussions since available copies are not in English.
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