  We construct a theory of hydrodynamic transport for systems with conserved
dipole moment, U(1) charge, energy, and momentum. These models have been
considered in the context of fractons, since their elementary and isolated
charges are immobile by symmetry, and have two known translation-invariant
gapless phases: a "p-wave dipole superfluid" phase where the dipole symmetry is
spontaneously broken and a "s-wave dipole superfluid" phase where both the U(1)
and dipole symmetries are spontaneously broken. We argue on grounds of symmetry
and thermodynamics that there is no transitionally-invariant gapless fluid with
unbroken dipole symmetry. In this work, we primarily focus on the hydrodynamic
description of p-wave dipole superfluids, including leading dissipative
corrections. That theory has, in a sense, a dynamical scaling exponent $z=2$,
and its spectrum of fluctuations includes novel subdiffusive modes $\omega \sim
-i k^4$ in the shear sector and magnon-like sound mode $\omega\sim \pm k^2 -i
k^2$. By coupling the fluid to background fields, we find response functions of
the various symmetry currents. We also present a preliminary generalization of
our work to s-wave dipole superfluids, which resemble $z=1$ fluids and feature
sound waves and diffusive shear modes, as in an ordinary fluid. However, the
spectrum also contains a magnon-like second-sound mode $\omega\sim \pm k^2 \pm
k^4 -i k^4$ with subdiffusive attenuation.
