  We present some exact solutions to the ideal hydrodynamics of a relativistic
superfluid with an almost-conformal equation of state. The solutions have
stress tensors which are invariant under Lorentz boosts in one direction, and
represent superfluid generalisations of the Bjorken and Gubser flows. We also
study corrections to the flows in first-order hydrodynamics, arguing that
dissipation is dominated by the shear viscosity. We present some simple
numerical solutions for these viscous corrections. Finally, we estimate the
size of corrections to the flows arising when the spontaneously broken
$\mathrm{U}(1)$ symmetry responsible for superfluidity is only approximate,
giving the corresponding Goldstone boson a small non-zero mass. We find that
the massless solutions can still provide good approximations at sufficiently
small spatial rapidities.
