Observational constraints of a new unified dark fluid and the $H_0$
  tension
  Unified cosmological models have received a lot of attention in astrophysics
community for explaining both the dark matter and dark energy evolution. The
Chaplygin cosmologies, a well known name in this group have been investigated
matched with observations from different sources. Obviously, Chaplygin
cosmologies have to obey restrictions in order to be consistent with the
observational data. As a consequence, alternative unified models, differing
from Chaplygin model, are of special interest. In the present work we consider
a specific example of such a unified cosmological model, that is quantified by
only a single parameter $\mu$, that can be considered as a minimal extension of
the $\Lambda$-cold dark matter cosmology. We investigate its observational
boundaries together with an analysis of the universe at large scale. Our study
shows that at early time the model behaves like a dust, and as time evolves, it
mimics a dark energy fluid depicting a clear transition from the early
decelerating phase to the late cosmic accelerating phase. Finally, the model
approaches the cosmological constant boundary in an asymptotic manner. We
remark that for the present unified model, the estimations of $H_0$ are
slightly higher than its local estimation and thus alleviating the $H_0$
tension.
