  We present and constrain a cosmological model where the only component is a
pressureless fluid with bulk viscosity as an explanation for the present
accelerated expansion of the universe. We study the particular model of a bulk
viscosity coefficient proportional to the Hubble parameter. The model is
constrained using the SNe Ia Gold 2006 sample, the Cosmic Microwave Background
(CMB) shift parameter R, the Baryon Acoustic Oscillation (BAO) peak A and the
Second Law of Thermodynamics (SLT). It was found that this model is in
agreement with the SLT using only the SNe Ia test. However when the model is
constrained using the three cosmological tests together (SNe+CMB+BAO) we found:
1.- The model violates the SLT, 2.- It predicts a value of H_0 \approx 53 km
sec^{-1} Mpc^{-1} for the Hubble constant, and 3.- We obtain a bad fit to data
with a \chi^2_{min} \approx 532. These results indicate that this model is
viable just if the bulk viscosity is triggered in recent times.
