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free surface flow; incompressible Navier-Stokes; shallow water approximation; hydrostatic approximation; closed water pipe; open channel; friction
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.
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