A pressurized model for compressible pipe flow.

We present the full derivation of a compressible model in a thin closed water pipe including friction, changes of section and slope variation. Starting from the compressible 3D Navier-Stokes equation under ”thin layer ” assumptions with well-suited boundary conditions, we justify the 1D reduced model called pressurized model (also named the P-model). It was introduced in the general framework of unsteady mixed flows in closed water pipes. This model describes the evolution of a compressible flow close to gas dynamics equations in a nozzle. We also propose a class of averaged low Oser compressible models of a general barotropic law p(ρ) = ργ, γ> 1