Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Bernoulli's relationship



There is an important conceptual error in my earlier posting.
The important dissipative agent in this problem is likely
turbulence, not viscosity. The argument remains the same since
it is based only on the existence of a dissipative agent, The
employment of an average velocity is more appropriate to the
case of turbulent flow in the channel. It is also the case
that Bernoulli arguments are not germane to dissipative *or*
turbulent flow problems. Just forget about them.

Anyway, here's my reply to John Denker's earlier posting. I
lost it on my messy desktop.

At 05:34 PM 11/8/00 -0800, Leigh Palmer wrote:

[Argument I haven't read which leads to contrary result, followed by:]

It would be more polite to read what I wrote before contradicting me.

I apologize. Your observation is correct. I am frequently
impolite, but I did not intend to be that time. Sorry.

Sometimes I see an evident fallacy in an answer (e.g. a
violation of the first or second law of thermodynamics) given
to a question and I dismiss it for that reason. I thought
(and I still think) that I had seen such a fallacy in your
answer. I'll go back and look to see where the problem arose
if I have to, but I was rushed when I wrote that reply, so
simply seeing that the answer was unphysical was sufficient.
I didn't have to check to find the origin of the final error.

Remarks: The foregoing answer is the obvious answer, and the only answer
consistent with relativity and symmetry and other basic principles.

It sure ain't obvious to me!

Further to my terse remark. As I pointed out in my discussion
of the problem counterintuitive consequences arise naturally
when the analysis is carried out physically. Robert Cohen seems
to have appreciated that. I was certainly surprised when I did
my analysis. I'm not an expert in this area (and I'm sure Robert
isn't either), but surely the limited physics I do know should
be of some help in resolving problems in it.

It remains obvious to me. The last time I went flying, altimeters (which
essentially measure static pressure) were known to indicate the same value
regardless of airspeed. This is important: when somebody asks Tower for
permission to overfly the field at 1500 feet, Tower would like some
assurance that that represents 1500 real feet, not something that is off by
hundreds of feet depending on airspeed.

Utterly irrelevant!

I'm very sorry that I haven't the macho pilot's background you
have, John. I don't think that disqualifies me or my argument. My
experience with cleaning rain gutters with a running hose and my
application of physical reasoning are probably more valuable
qualifications, anyway.

The situation Professor Cohen asked about is a thinly disguised variation
of the same physics.

I think you forgot about continuity, John.

I didn't.

You've got water accelerating in a trough under the influence of viscosity,

Here, in retrospect, I should have written "a dissipative force"
instead of "viscosity".

I indicated the pattern of pressure, taking viscosity into account. I
didn't mention velocity at all, because it didn't matter. If you want to
worry about velocity, you will find a velocity pattern that is consistent
with this pressure pattern. And with continuity.

and then slowing down as it goes through a propeller.

I idealized the propeller as a pump. It increases the pressure in just the
way I indicated. My idealization removes all kinds of complicated jets and
countercurrents. I don't think anybody on this list wants to see the
non-idealized version.

High velocity at pump inlet and low velocity at pump outlet is not at all
unusual.

This isn't a pump. There is no outlet pipe here, something that
is probably necessary to the case you cite here. Surely the outlet
pressure must be higher if the velocity of flow is lower. I know
that my model for the propeller does not admit of this possibility,
but do you really believe that a propeller in an open channel will
diminish the velocity of flow in the channel?

Continuity tells me that the product of cross sectional area and
velocity is constant. In your explanation the cross sectional area
diminishes with distance along the trough. A consequence is the
acceleration of the water. Surely viscosity cannot be the agent
responsible for this acceleration, so we are left with the
possibility that it derives from conversion of gravitational
potential energy. Now while I acknowledge that might happen above
some extreme surface elevation gradient, it is certainly not as
"obvious" to me that it must happen as it is to you.

I am simply trying to understand the problem Robert Cohen posed to
us. I'm looking forward to his reply to our postings, since he
also saw something counterintuitive in his own result.

Leigh