We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompressible Navier-Stokes equations under shallow water assumptions with prescribed "well-suited" boundary conditions.
@article{702962, title = {Dimension reduction for incompressible pipe and open channel flow including friction}, booktitle = {Application of Mathematics 2015}, series = {GDML\_Books}, publisher = {Institute of Mathematics CAS}, address = {Prague}, year = {2015}, pages = {17-33}, zbl = {06669916}, url = {http://dml.mathdoc.fr/item/702962} }
Ersoy, Mehmet. Dimension reduction for incompressible pipe and open channel flow including friction, dans Application of Mathematics 2015, GDML_Books, (2015), pp. 17-33. http://gdmltest.u-ga.fr/item/702962/