  An hydrodynamic description of a one-dimensional flow of an ideal Fermi fluid
is constructed from a semiclassical approximation. For an initially fully
degenerate fluid, Euler and continuity hydrodynamic equations are dual to two
uncoupled inviscid Burgers' equations. Yet the price for the initial simplicity
of the description is paid by the complexity of non-linear instabilities
towards possible turbulent evolutions. Nevertheless, it is shown that linear
long-wavelength density perturbations on a stationary flow are generically
stable. Consequently, linear sound obeys a wave equation with analogy to
gravity. The results have applications for ultra-cold atomic gases.
