  The dynamo effect is a class of macroscopic phenomena responsible for
generation and maintaining magnetic fields in astrophysical bodies. It hinges
on hydrodynamic three-dimensional motion of conducting gases and plasmas that
achieve high hydrodynamic and/or magnetic Reynolds numbers due to large length
scales involved. The existing laboratory experiments modeling dynamos are
challenging and involve large apparatuses containing conducting fluids subject
to fast helical flows. Here we propose that electronic solid-state materials --
in particular, hydrodynamic metals -- may serve as an alternative platform to
observe some aspects of the dynamo effect. Motivated by recent experimental
developments, this paper focuses on hydrodynamic Weyl semimetals, where the
dominant scattering mechanism is due to interactions. We derive Navier-Stokes
equations along with equations of magneto-hydrodynamics that describe transport
of Weyl electron-hole plasma appropriate in this regime. We estimate the
hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key
figure of merit of the dynamo mechanism. We show that it can be relatively
large to enable observation of the dynamo-induced magnetic field bootstrap in
experiment. Finally, we generalize the simplest dynamo instability model --
Ponomarenko dynamo -- to the case of a hydrodynamic Weyl semimetal and show
that the chiral anomaly term reduces the threshold magnetic Reynolds number for
the dynamo instability.
