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Re: [Phys-l] question about Bernoulli

In the scenario provided, there the end of the cylinder is open, with no
change in area, so I think talking about a constriction is changing the
subject (although I like the idea of considering a different reference
frame).

I've also noticed that everyone has assumed that the fluid will flow
INTO the hole (because the fluid velocity is greater inside the hole
than outside).

Suppose the end of the cylinder was closed. The fluid would most
certainly flow OUT of the hole, right?

What if there was a small opening at the end of the cyclinder (like a
syringe). Would fluid still flow OUT of the hole or would it flow INTO
the hole?

If OUT, what size opening would lead the fluid to flow INTO the hole vs.
OUT?

[Also, does the argument depend on whether the fluid is compressible or
incompressible?]

----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@po-box.esu.edu http://www.esu.edu/~bbq

-----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 the
*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
there. But my
question is really just about the fact that one might seem to get
different answers to the question, "Where is the pressure higher?"
depending on the inertial frame in which one applies the
Bernoulli eqn.
Obviously that can't be, so what is wrong with the argument?

John Mallinckrodt
Cal Poly Pomona

Carl Mungan wrote:

John M wrote:

The Bernoulli equation (for incompressible fluids) says
that the sum
of the
kinetic energy density, the gravitational potential
energy density,
and the
pressure is constant along a streamline so that if the speed
DECREASES from
point A to point B along a horizontal streamline, the
pressure must
be HIGHER
at point B than at point A.

But in the rest frame of the fluid at point A, the speed
is zero at
point A and, thus, necessarily is higher at point B so
that, in THAT
frame, 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 outside
(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
be shaped as
follows, extending to + and - infinity and filled with fluid:

------
/
/
---

A B

---
\
\
------

Now to turn on the fluid motion. But in A's frame, the
fluid is at
rest. But the pipe moves to the right. That pushes on fluid
in region
B, so that it starts to move, but obviously somewhat slower
than the
pipe. It is the diagonal portion of the pipe (where it is
increasing
in diameter) that sweeps out volume that must push fluid in
B forward.
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
continuity requires.
We now have some kind of "ramjet" arrangement, recorded as
a pressure
back 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
moves past
the viscosity-free (superfluid) liquid.

Am I on the right track in the kind of thinking you were
expecting
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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