Re: Bernoulli's equation

[Bob Sciamanda <trebor@VELOCITY.NET>]

I would speak in terms of the buildup of "back-pressure" resulting from
changes in the constraints imposed on the flowing fluid by the geometry of
the pipe.
Eg.: At a bend in the pipe, a back pressure of fluid "piling up" at the
bend adds a "centripetal pressure" - the same thing happens to the flow of
electrical current in a bent wire (surface charges build up).
Similarly a diminution of pipe size will create a bottleneck - as the
fluid tends to "pile up" at the bottleneck a back pressure is created.
This is a very palpable phenomenon:  you can feel the increase in pressure
in a water hose as you manually restrict the final opening.
(I don't appreciate your wish to have  the "equipartition theorem come
into play here" - keep it simple - it is!

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Wolfgang Rueckner" <rueckner@FAS.HARVARD.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, January 10, 2002 2:01 PM
Subject: Bernoulli's equation


> I'm curious if anyone out there has a good explanation (appropriate
> for introductory algebra-based physics students) of why there is a
> decrease in pressure with an increase in velocity from a molecular
> point of view (a kinetic theory of gases kind of argument).
>
> I explain to the class how Bernoulli's equation is a statement of
> conservation of energy (the pressure-volume work, gravitational
> potential energy, and kinetic energy terms) and the students see how
> it follows from the equation that one must have a decrease in
> pressure accompany an increase in velocity.  I also invoke an
> argument similar to Epstein's (from his book Thinking Physics) in
> which one imagines a tiny submarine moving in the fluid inside a
> pipe:  when there's a transition from a large diameter pipe to a
> smaller diameter, the fluid of course increases in speed (continuity
> equation), and one can argue that there must be a difference in
> pressure (a net force) to accelerate the submarine and fluid.  Thus
> the pressure must be less in the region where the pipe gets smaller
> compared to the region behind the sub where the pipe is larger.
>
> I'd like to understand this from a microscopic point of view.  Does
> the equipartition theorem come into play here?  I look forward to
> reading your ideas.
>
> Thanks, Wolfgang