  To quantify the effect that bar driven mass inflow can have on the evolution
of a galaxy requires an understanding of the dynamics of the inflowing gas. In
this paper we study the kinematics of the dense molecular gas in a set of seven
barred spiral galaxies to determine which dynamical effects dominate. The
kinematics are derived from observations of the CO J=(1-0) line made with the
Berkeley-Illinois-Maryland Association (BIMA) millimeter array. We compare the
observed kinematics to those predicted by ideal gas hydrodynamic and ballistic
cloud-based models of gas flow in a barred potential. The hydrodynamic model is
in good qualitative agreement with both the current observations of the dense
gas and previous observations of the kinematics of the ionized gas. The
observed kinematics indicate that the gas abruptly changes direction upon
entering the dust lanes to flow directly down the dust lanes along the leading
edge of the bar until the dust lanes approach the nuclear ring. Near the
location where the dust lanes intersect the nuclear ring, we see two velocity
components: a low velocity component, corresponding to gas on circular orbits,
and a higher velocity component, which can be attributed to the fraction of gas
flowing down the bar dust lane which sprays past the contact point toward the
other half of the bar. The ballistic cloud-based model of the ISM is not
consistent with the observed kinematics. The kinematics in the dust lanes
require large velocity gradients which cannot be reproduced by an ISM composed
of ballistic clouds with long mean-free-paths. Therefore, even the dense ISM
responds to hydrodynamic forces.
