The system of balance laws describing a compressible fluid flow
in a nozzle forms a non-strictly hyperbolic system of partial
differential equations which, also, is not fully conservative
due to the effect of the geometry. First, we investigate the
general properties of the system and determine all possible wave
combinations. Second, we construct analytically the solutions of
the Riemann problem for any values of the left-and right-handed
states. For certain values we obtain up to three solution whose
structure is carefully described here. In some range of Riemann
data, no solutions exists. When three solutions are avialable,
then exactly one of them contains two stationary waves which are
superimposed in the physical space. We include also numerical plots
of these solutions.