  --In this article we study the hydrodynamic spectrum of a superfluid confined
in a cylindrical trap. We show that the dispersion relation $\omega$(q) of the
phonon branch scales like $\sqrt$ q at large q, leading to a vanishingly small
superfluid critical velocity. In practice the critical velocity is set by the
breakdown of the hydrodynamic approximation. For a broad class of superfluids,
this entails a reduction of the critical velocity by a factor ($\omega$ $\perp$
/\"i1/2c) 1/3 with respect to the free-space prediction (here $\omega$ $\perp$
is the trapping frequency and \"i1/2c the chemical potential of the cloud).
