Liu hard disk equation of state

The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1 of

$Z={\frac {1+\eta ^{2}/8-\eta ^{4}/10}{(1-\eta )^{2}}}$

$Z={\frac {1+\eta ^{2}/8+\eta ^{4}/18-\eta ^{4}/21}{(1-\eta )^{2}}}$

where the packing fraction is given by $\eta =\pi \rho \sigma ^{2}/4$ where $\sigma$ is the diameter of the disks.