Non conservative products in fluid dynamics

Fluid flow in pipes with discontinuous cross section or kinks is described through balance laws a non conservative product the source. At jump discontinuities pipes’ geometry, physics of problem suggests how to single out solution. On this basis, we present definition solution for general BV geometry and prove an existence result, consistent limiting procedure from piecewise constant geometries. In case smoothly curved pipe thus justify appearance curvature source term linear momentum equation. These results are obtained as consequences result devoted abstract terms resonant case.