  By considering the stability of potential flow of a superfluid around large
obstacles of size R, we derive an analytical result for the critical velocity
which is of order v_c \sim \hbar / mR, scaling inversely with obstacle size, in
contrast to what is obtained from a Landau criterion. Our results are compared
with numerical solutions of the Gross-Pitaevskii equation and with recent
measurements of the critical velocity in Bose-Einstein condensates of dilute
atomic gases.
