  One-dimensional hard rod gases are explicitly constructed as the limits of
discrete systems: exclusion processes involving particles of arbitrary length.
Those continuum many-body systems in general do not exhibit the same
hydrodynamic properties as the underlying discrete models. Considering as
examples a hard rod gas with additional long-range interaction and the
generalized asymmetric exclusion process for extended particles ($\ell$-ASEP),
it is shown how a correspondence between continuous and discrete systems must
be established instead. This opens up a new possibility to exactly predict the
hydrodynamic behaviour of this continuum system under Eulerian scaling by
solving its discrete counterpart with analytical or numerical tools. As an
illustration, simulations of the totally asymmetric exclusion process
($\ell$-TASEP) are compared to analytical solutions of the model and applied to
the corresponding hard rod gas. The case of short-range interaction is treated
separately.
