We simulate the flow of gas in the Binney et al. model of the bar at t
he centre of the Milky Way. We argue that the flow of a clumpy interst
ellar medium is most realistically simulated by a sticky-particle sche
me, and investigate two such schemes. In both schemes orbits close to
the cusped orbit rapidly become depopulated. This depopulation places
a lower limit on the pattern speed since it implies that in the (l,v)
plane the cusped orbit lies significantly inside the peak of the HI te
rminal-velocity envelope at l similar or equal to 2 degrees. We find t
hat the size of the central molecular disc and the magnitudes of the o
bserved forbidden velocities constrain the eccentricity of the Galacti
c bar to values similar to that arbitrarily assumed by Binney et al. W
e study the accretion by the nuclear disc of matter shed by dying bulg
e stars. We estimate that mass loss by the bulge can replenish the HI
in the nuclear disc within two bar rotation periods, in good agreement
with the predictions of the simulations. When accretion of gas from t
he bulge is included, fine-scale irregular structure persists in the n
uclear disc. This structure gives rise to features in longitude-veloci
ty plots which depend significantly on viewing angle, and consequently
give rise to asymmetries in longitude. These asymmetries are, however
, much less pronounced than those in the observational plots. We concl
ude that the addition of hydrodynamics to the Binney et al. model does
not resolve some important discrepancies between theory and observati
on. The model's basic idea does, however, have high a priori probabili
ty and has enjoyed some significant successes, while a number of poten
tially important physical processes - most notably the self-gravity of
interstellar gas - are neglected in the present simulations. In view
of the deficiencies of our simulations and interesting parallels we do
observe between simulated and observational longitude-velocity plots,
we believe it would be premature to reject the Binney et al. model pr
ior to exploring high-quality three-dimensional simulations that inclu
de self-gravitating stars and gas.