  We develop the hydrodynamic theory for number conserving asymmetric exclusion
processes with short-range random quenched disordered hopping rates, which is
one-dimensional Kardar-Parisi- Zhang (KPZ) equation with quenched columnar
disorder. We show that when the system is away from half-filling, the universal
spatio-temporal scaling of the density fluctuations is indistinguishable from
its pure counterpart, with the model belonging to the one-dimensional
Kardar-Parisi-Zhang universality class. In contrast, close to half-filling, the
quenched disorder is relevant, leading to a new universality class. We
physically argue that the irrelevance of the quenched disorder when away from
half-filling is a consequence of the averaging of the disorder by the
propagating density fluctuations in the system. In contrast, close to
half-filling the density fluctuations are overdamped, and as a result, are
strongly influenced by the quenched disorder.
