  Based on the collision rules for hard needles we derive a hydrodynamic
equation that determines the coupled translational and rotational dynamics of a
tagged thin rod in an ensemble of identical rods. Specifically, based on a
Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig
projection formalism is used to derive a continued fraction representation for
the correlation function of the tagged particle's density, specifying its
position and orientation. Truncation of the continued fraction gives rise to a
generalised Enskog equation, which can be compared to the phenomenological
Perrin equation for anisotropic diffusion. Only for sufficiently large density
do we observe anisotropic diffusion, as indicated by an anisotropic mean square
displacement, growing linearly with time. For lower densities, the Perrin
equation is shown to be an insufficient hydrodynamic description for hard
needles interacting via binary collisions. We compare our results to
simulations and find excellent quantitative agreement for low densities and
qualtitative agreement for higher densities.
