  We report on numerical solutions of the Gross-Pitaevskii equation for
two-dimensional flow of a superfluid condensate through a small orifice. Above
a critical velocity of about $30\%$ of the speed of sound, cavitation occurs in
the throat of the orifice. The cavitating bubbles form the cores of singly
quantized vortices which detach from the boundary and are convected downstream.
