Re: pressure-energy density

[Leigh Palmer <palmer@sfu.ca>]

> Hi Folks,
>
> The Bernouli equation is that
>
>               P + (1/2)mv^2 + mgh
>
> where m is the mass per unit volume, is constant along a streamline of a
> viscosity-less incompressible fluid undergoing laminar flow.  Does
> thinking of the pressure P as some kind of pressure-energy density to be
> encouraged, or does is lead to later difficulties?  Since the fluid is
> incompressible, it is clear that P does not represent work per unit volume
> done in compressing the fluid.

Thinking of the pressure as a potential energy density is perfectly
reasonable here. It should not be reified, however. Thinking of
energy as "stuff" leads to some cognitive errors as we have seen in
the energy flow discussion. Always keep that caveat in mind.

I notice that you did not ask if one could think of mgh (I'd prefer
rho*g*h) as a potential energy density. Surely that is no different
from pressure. Why are you more comfortable with one than with the
other? Both are formal expressions that represent non-localized
energy densities. Only the kinetic term can lay any claim to being
local.

Leigh