Simulations of three-dimensional cavitating flows for an orifice fed by a manifold are performed using a homogeneous flow model The dynamics of a bubble response per the Rayleigh-Plesset equation are cast into a constitutive equation for the density for the pseudo-fluid. Results are obtained for several different cross-flow velocities for both cavitating and noncavitating flows. The model shows good agreement with measured discharge coefficients and also reveals vortex structures recently found in experimental observations.