  A generally parameterized equation of state (EOS) is investigated in the
cosmological evolution with bulk viscosity media modelled as dark fluid, which
can be regarded as a unification of dark energy and dark matter. Compared with
the case of the perfect fluid, this EOS has possessed four additional
parameters, which can be interpreted as the case of the non-perfect fluid with
time-dependent viscosity or the model with variable cosmological constant. From
this general EOS, a completely integrable dynamical equation to the scale
factor is obtained with its solution explicitly given out. (i) In this
parameterized model of cosmology, for a special choice of the parameters we can
explain the late-time accelerating expansion universe in a new view. The early
inflation, the median (relatively late time) deceleration, and the recently
cosmic acceleration may be unified in a single equation. (ii) A generalized
relation of the Hubble parameter scaling with the redshift is obtained for some
cosmology interests. (iii) By using the SNe Ia data to fit the effective
viscosity model we show that the case of matter described by $p=0$ plus with
effective viscosity contributions can fit the observational gold data in an
acceptable level
