  Using the recently developed approach to quantum Hall physics based on
Newton-Cartan geometry, we consider the hydrodynamics of an interacting system
on the lowest Landau level. We rephrase the non-relativistic fluid equations of
motion in a manner that manifests the spacetime diffeomorphism invariance of
the underlying theory. In the massless (or lowest Landau level) limit, the
fluid obeys a force-free constraint which fixes the charge current. An entropy
current analysis further constrains the energy response, determining four
transverse response functions in terms of only two: an energy magnetization and
a thermal Hall conductivity. Kubo formulas are presented for all transport
coefficients and constraints from Weyl invariance derived. We also present a
number of Streda-type formulas for the equilibrium response to external
electric, magnetic and gravitational fields.
