  We set up the construction of generic (d+2)-dimensional metrics corresponding
to (d+1)-dimensional fluids, representing holographically the hydrodynamic
regimes of the putative dual theories. We give general seed equilibrium metrics
appropriate to generic bulk stress energy tensors and discuss the implications
of conformal rescalings of the hypersurface on which the fluid is defined. We
then show how to obtain the corresponding hydrodynamic metrics using a
relativistic gradient expansion and discuss the integrability conditions of the
resulting equations. The stress energy tensors of the resulting fluids, both at
and away from equilibrium, satisfy a quadratic constraint. We interpret this
constraint in terms of two possible equations of state for the fluid and show
that only one of the two equations is physical. We illustrate our discussions
with the example of the cutoff AdS fluid, for which we find the precise
interpretation in terms of deformations of the UV conformal field theory.
Finally we discuss the relation between the modern fluid/gravity approach taken
in this paper and the earlier membrane paradigm.
