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 the Λ 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 the Λ CDM model.