  We run hydrodynamical simulations of a 2D isothermal non self-gravitating
inviscid gas flowing in a rigidly rotating externally imposed potential formed
by only two components: a monopole and a quadrupole. We explore systematically
the effects of varying the quadrupole while keeping fixed the monopole and
discuss the consequences for the interpretation of longitude-velocity diagrams
in the Milky Way. We find that the gas flow can constrain the quadrupole of the
potential and the characteristics of the bar that generates it. The exponential
scale length of the bar must be at least $1.5\rm\, kpc$. The strength of the
bar is also constrained. Our global interpretation favours a pattern speed of
$\Omega=40\,\rm km s^{-1} {kpc}^{-1}$. We find that for most observational
features, there exist a value of the parameters that matches each individual
feature well, but is difficult to reproduce all the important features at once.
Due to the intractably high number of parameters involved in the general
problem, quantitative fitting methods that can run automatic searches in
parameter space are necessary.
