  In highly conductive metals with sufficiently strong momentum-conserving
scattering, the electron momentum is regarded as a long-lived quantity, whose
dynamics is described by an emergent hydrodynamic theory. In this paper, we
develop an electron hydrodynamic theory for noncentrosymmetric metals, where a
novel class of electron fluids is realized by lowering crystal symmetries and
the resulting geometrical effects. The obtained hydrodynamic equation suggests
a nontrivial analogy between electron fluids in noncentrosymmetric metals and
chiral fluids in vacuum, and predicts novel hydrodynamic transport phenomena,
that is, asymmetric Poiseuille flow and anomalous edge current. Our theory also
gives a hydrodynamic description of the counterpart of various anomalous
transport phenomena such as the quantum nonlinear Hall effect. Furthermore, we
give a symmetry consideration on the hydrodynamic equation and propose several
experimental setups to realize such anomalous hydrodynamic transport in the
existing hydrodynamic materials, including bilayer graphene and Weyl
semimetals.
