  We analyze the Navier Stokes equation, and show that all non-viscous,
irrotational flows are barotropic. As far as we know, this has never been
stated in the literature before, and indirectly suggests that vorticity is
required to make these flows non-barotropic. Both the pressure, temperature,
speed, entropy, enthalpy, and a Bernoulli function are derived to be only
functions of the density (which is a function of space and time). When we also
require steady flow, the Bernoulli function is a constant in all space, not
just on streamlines.
