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-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of Carl Mungan
Sent: Saturday, November 20, 2010 10:07 AM
To: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] question about Bernoulli
Oops, you guys are right (haven't seen Bryan's message yet -
presumably it'll be in the digest). My fault because
originally I was thinking of the pipe oriented the other way
around and had A and B at different points and so on, so I
got things mixed up now. I was hoping that I could say some
extra work (the pressure really starts life in the Bernoulli
equation as *work* and we know work is frame
dependent) is done by the diagonally sloped portion of the
pipe since it is now moving and hence has a displacement.
I'll try to straighten out my thinking and see if I make any
headway (before the digest appears and probably gives me more
hints if not a solution). -Carl
I think Bryan is right that you mean to have the pipe moving to thethere. But my
*left* and the fluid at B would also be moving to the left at a
somewhat slower speed. I'm not sure where you'd go from
question is really just about the fact that one might seem to getBernoulli eqn.
different answers to the question, "Where is the pressure higher?"
depending on the inertial frame in which one applies the
Obviously that can't be, so what is wrong with the argument?that the sum
John Mallinckrodt
Cal Poly Pomona
Carl Mungan wrote:
John M wrote:
The Bernoulli equation (for incompressible fluids) says
energy density,of the
kinetic energy density, the gravitational potential
pressure mustand the
pressure is constant along a streamline so that if the speed
DECREASES from
point A to point B along a horizontal streamline, the
is zero atbe HIGHER
at point B than at point A.
But in the rest frame of the fluid at point A, the speed
that, in THATpoint A and, thus, necessarily is higher at point B so
be outsideframe, the pressure must be LOWER at point B than at point A.
What's up with that?
----------
Hmm, that is a good question. My first thought goes as follows: I
suppose point A to be inside a constriction and point B to
be shaped as(let's say downstream and call that the +x direction) of the
constriction. I'll take the fluid to be incompressible and to have
zero viscosity.
Start with everything at rest and visualize the tube to
fluid is atfollows, extending to + and - infinity and filled with fluid:
------
/
/
---
A B
---
\
\
------
Now to turn on the fluid motion. But in A's frame, the
in regionrest. But the pipe moves to the right. That pushes on fluid
than theB, so that it starts to move, but obviously somewhat slower
increasingpipe. It is the diagonal portion of the pipe (where it is
B forward.in diameter) that sweeps out volume that must push fluid in
continuity requires.We will thus get precisely that the speed of fluid in B equals the
ratio of area of region B to area of region A, as
a pressureWe now have some kind of "ramjet" arrangement, recorded as
moves pastback on the diagonal portion of the pipe and hence as a pressure in
region B. But there is no pressure in region A as the pipe
expectingthe viscosity-free (superfluid) liquid.
Am I on the right track in the kind of thinking you were
for a solution? Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729
(F) Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
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