  In this paper, we study the equation of state admissible for a flat FRW
models filled with a bulk viscous fluid by using the Lie group method. It is
founded that the model admits scaling symmetries iff the bulk viscous parameter
$\gamma =1/2$. In this case, it is found that the main quantities follow a
power law solution and in particular the bulk viscous pressure $\Pi $ has the
same order of magnitude as the energy density $\rho ,$ in such a way that it is
possible to formulate the equation of state $\Pi =\varkappa \rho ,$ where
$\varkappa \in \mathbb{R}^{-}$ (i.e. is a negative numerical constant)$.$ If we
assume such relationship we find again that the model is scale invariant iff
$\gamma =1/2.$ We conclude that the model accepts a scaling symmetry iff
$\gamma =1/2$ and that for this value of the viscous parameter, $\Pi =\varkappa
\rho ,$ but the hypothesis $\Pi =\varkappa \rho $ does not imply $\gamma =1/2,$
and that the model is scale invariant.
