  We consider in this work the different possible stationary flows of a one
dimensional quantum fluid in the mean-field regime. We focus on the supersonic
regime where a transition from a time dependent flow to a stationary
diffractive flow occurs at a given critical velocity. We give nonperturbative
results for this critical velocity in the presence of a localised obstacle of
arbitrary size and strength. In addition, we discuss the existence of
superfluid-like solution in the supersonic regime due to resonant transport and
provide a complete map of the different regimes of stationary transport of a
quantum fluid.
