Re: Bernoulli (horizontal)

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Fri, 16 Nov 2001, Ludwik Kowalski wrote:

> Is it OK to say that P is also the energy per unit volume
> (because N/m^2=J/m^3)? We know that P decreases along the tube
> as the cross sectional area becomes smaller. The situation
> looks like an energy transformation; process. Bernoulli tells
> us that P decreases by the same amount by which the KE (also
> per unit volume) increases. What is wrong with saying that P
> is the "mechanical energy of pressure," per unit volume? Is
> this energy kinetic or potential?

Here are a few considerations that I think you will find argue
against considering pressure itself as an energy density:

1. If the pressure of an incompressible fluid is to properly
represent some form of energy density, you ought to be able to
come up with a raft of processes where that form of energy is lost
and other, more well known forms appear in its place.

2. You ought to be able to account for that energy in all
processes.  Consider, for instance, a 1 cm^3 diamond under 50
kbars of pressure.  What happens to those 5000 J of "pressure
energy" when the pressure is removed?

3. The internal energy density of air at room temperature is about
3.5p by virtue of the fact that it is essentially a diatomic gas.
In general, the internal energy density of a gas will depend on
what kind of gas it is and the temperature and can always be
expressed as some number times p simply because p has *units* of
energy density.  But how does all this square with the idea of p
itself *as* an energy density?

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm