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I am thinking of a volume element of the fluid moving along a streamline
in a region occupied by the Earth's gravitational field, which is
conservative. Conservative fields have potential energy functions so it
seems OK to me to think of mgh as the potential energy per unit volume
associated with the volume element of fluid. Also, if I think of the
Earth-volume-element system the gravitational potential energy of the
system is clearly a function of the system's configuration, a requirement
for any potential energy.
I am less comfortable with thinking of P as pressure-energy density
because I am unable to construct a picture analogous to the one I just
described for the gravitational-energy density.
The lack of localness of the gravitational-potential-energy density can be
dealt with, to a degree, by considering the potential field associated
with the gravitational field of the Earth.