  We consider hydrodynamic electron transport in the Hall-bar geometry. The
theory is developed for systems with non-Galilean-invariant electron liquids.
We show that inhomogeneity of the electron density induced by long-range
disorder and gating leads to mixing between the hydrodynamic transport mode and
transport relative to the electron liquid. For graphene systems near charge
neutrality, these effects lead to strong coupling of the hydrodynamic flow to
charge transport. As a result, the effective electrical conductivity of the
system may significantly exceed the intrinsic conductivity of the electron
liquid. We obtain analytic expressions for the thermoelectric transport
coefficients of the system as a function of density in the full crossover
region between clean and disorder-dominated regimes.
