  Some cosmological scenarios with bulk viscosity for the dark energy fluid are
considered. Based on some considerations related to hydrodynamics, two
different equations of state for dark energy are assumed, leading to power-law
and logarithmic effective corrections to the pressure. The models are tested
with the latest astronomical data from Type Ia supernovae (Pantheon sample),
measurements of the Hubble parameter $H(z)$,
  Baryon Acoustic Oscillations and Cosmic Microwave Background radiation. In
comparison with $\Lambda$CDM model, some different results are obtained and
their viability is discussed. The power-law model shows some modest results,
achieved under negative values of bulk viscosity, while the logarithmic
scenario provide good fits in comparison to $\Lambda$CDM model.
