  The concept of local pressure is pivotal to describe many important physical
phenomena, such as buoyancy or atmospheric phenomena, which always require the
consideration of space-varying pressure fields. These fields have precise
definitions within the phenomenology of hydro-thermodynamics, but a simple and
pedagogical microscopic description based on Statistical Mechanical is still
lacking in present literature. In this paper, we propose a new microscopic
definition of the local pressure field inside a classical fluid, relying on a
local barometer potential that is built into the many-particle Hamiltonian.
Such a setup allows the pressure to be locally defined, at an arbitrary point
inside the fluid, simply by doing a standard ensemble average of the radial
force exerted by the barometer potential on the gas' particles. This setup is
further used to give a microscopic derivation of the generalized Archimedes's
buoyancy principle, in the presence of an arbitrary external field. As
instructive examples, buoyancy force fields are calculated for ideal fluids in
the presence of: i) a uniform force field, ii) a spherically symmetric harmonic
confinement field, and iii) a centrifugal rotating frame.
