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Re: [Phys-l] question about Bernoulli

Temperature depends on kinetic energy. In normal circumstances, impelling air to flow in one direction need not increase its temperature.

This implies that a speed vector surface describing the speed (and hence indirectly, kinetic energy) of all molecules in any direction does not change its diameter when the air column is moved in one direction. But the mean molecule is not now centered on this sphere, because a piston is contributing a linear speed component - to ALL possible molecular speed vector directions on average.
It is that linear component that is making the formerly transverse paths around a diameter of constant speed, now forward slanting, so that the new transverse component is less than before. Or, perhaps I can put it another way - when the air column is moving, the air particle impact normal to the sidewall surface is the resultant of a speed vector pointing at a backward slope to the rear, with a forwards component due to the column speed forward. This is shorter than the speed represented by a diameter.

Or so I assert! :-)

B

On 11/17/2010 5:57 PM, William Robertson wrote:
I'm not completely sure I understand the visual, but my impression is that once you change the movement in one direction, you no longer have a sphere for your speed direction vectors. You haven't changed the transverse speeds with your actions. Am I misinterpreting your visual?

Bill


William C. Robertson, Ph.D.
Bill Robertson Science, Inc.
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On Nov 17, 2010, at 4:20 PM, brian whatcott wrote:

Here's a Just-so explanation, offered without much corroboration.

The current theory relating pressure and temperature in gases, due to
Clausius,
has it that the kinetic energy of molecules impacting container walls
determines the mean pressure on those surfaces.

Visualize a spherical surface plotting the (probable, mean, rms??)
speed direction vectors of the cumulative air molecule, located at its
center.

If the molecules are all moved in one direction, the spherical surface
is displaced
forward by that displacement rate vector, with the effect that the
mean molecule is
now off centered in its sphere, the mean molecule trailing the center
of its speed
vector sphere.

The transverse distance from the molecule to the sphere's speed vector
surface is now
reduced from a radius, to some lesser value. It was this transverse
set of trajectories
that contributed the usual pressure, and it is this set of slower
transverse trajectories
that now provide a reduced side wall pressure.
The pressure being proportional to kinetic energy, this pressure drops
with the
drop in the square of this transverse speed.

This is a fairly concrete vivid image, no doubt. However - no guarantees.


Brian W


On 11/17/2010 3:04 PM, William Robertson wrote:
I have for some time strived to explain the Bernoulli effect in terms
of what's happening at the molecular level. We all know the
mathematical explanation that leads to higher velocities being
associated with lower pressures, but I want something that does not
rely on the mathematics. In other words, what are the molecules doing
that leads to the Bernoulli effect? /snip/
Bill


William C. Robertson, Ph.D.

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