  We add extreme driving to the Kob-Andersen kinetically-constrained
lattice-gas model in order to mimic the effect of gravity on dense granular
systems. For low particle densities, the current that develops in the system
agrees at arbitrary field intensity with a mean field theory. At intermediate
densities, spatial correlations give rise to non-monotonic dependence of the
current on field intensity. At higher densities, the current ultimately
vanishes at a finite, field-dependent jamming density. We supplement the study
of this bulk behavior with an investigation of the current through a narrow
hole. There, lateral flow decreases the local density in front of the hole.
Remarkably, the current through the hole quantitatively agrees with a
theoretical prediction based on the bulk current at the measured local density.
