  We apply a homogenization process to the acoustic velocity potential wave
equation. The study of various examples shows that the resulting effective
properties are different from those of the homogenized pressure wave equation
for the same underlying acoustic parameters. A careful analysis reveals that a
given set of inhomogeneous parameters represents an entirely different physical
system depending on the considered equation. Our findings unveil a different
way of tailoring acoustic properties through gradients of the static pressure.
In contrast to standard metafluids based on isobaric composites, this
alternative kind of metafluids is suitable for the implementation of
transformational devices designed via the velocity potential equation. This
includes acoustic systems in a moving background or arising from general
space-time transformations. As an example, we design a device able to cloak the
acoustic velocity potential.

General Relativity and Quantum Cosmology;Mesoscale and Nanoscale Physics;Materials Science;Classical Physics