Re: [Phys-l] Bernoulli's Principle

[John Denker <jsd@av8n.com>]

On 12/20/2007 03:48 PM, Richard Blade wrote:

> Clearly there is a flaw in my conceptualization.  The question is: where?

There are multiple misconceptions.

> Following the advice of Richard Feynman, I always try to conceptualize 
> physical phenomena using as many different models as I can.

That's a misconception already.  Feynman had a formidable
conceptual intuition ... but he also had formidable analytical
skills.  The celebrated Feynman diagrams are characteristic:
the diagrams allow you to visualize the calculation.  The
diagrams tell you what integrals to do.  The diagrams are a
guide to the calculation, not a replacement for the calculation.

We agree it is good to look at things in multiple ways.  In
this case that means using the continuum fluid model *and* the
discrete particle model.

If a hand-wavy qualitative particle argument disagrees with a
careful quantitative fluid argument, it's obvious where the
problem lies.  The problem is not that particles are wrong;
the problem is that the particle model was not used carefully.

In particular, people generally have an intuition about particles
that is unhelpful when it comes to discussing ordinary fluids
such as air or water.  There is tremendous negative transference.
Their intuition underestimates by orders of magnitude the number
of particles, overestimates by orders of magnitude the size of
the particles, and underestimates by totally absurd margins the
importance of particle/particle interactions.  I call this the
"bullet fallacy".  For details, see
  http://www.av8n.com/how/htm/airfoils.html#sec-fluid

Bernoulli's principle is expressed in the language of continuum
fluids:  pressure, density, and velocity of flow.  Indeed Bernoulli
(Daniel, in this case) published the formula more than a century
before anybody had the slightest clue how big atoms were.  The
formula depends on first-order fluid properties that are insensitive
to the molecular substructure of the fluid.  Forsooth, as soon as
you start considering second-order "transport" properties such as
viscosity and/or thermal conductivity, Bernoulli's principle no
longer holds.

It is therefore exceedingly unlikely that any analysis of
Bernoulli's principle will shed any light on the nature of
atoms, or vice versa.  You're welcome to try, but don't be
surprised if the payoff is really, really small.

The conventional and sensible way to proceed is via a
step-by-step process:  Starting from atoms, connect the atoms
to the basic fluid properties such as pressure, density, and
velocity of flow.  Then as a second step, explain the Bernoulli
result in terms of /fluid/ properties.  Going directly from
atoms to Bernoulli is like trying to jump from the sidewalk
onto the roof.  I recommend using a ladder instead, taking it
one step at a time.

> The decrease in velocity in the y- and 
> z-directions means softer collisions with the pipe wall and thus lower 
> pressure. 

Different pressures in different directions?  This is just
the sort of misconception that never arises if you take the
time to develop a sensible theory of continuous fluids.  Even
before Bernoulli's time it had been known for a century that
pressure was a scalar i.e. the same in all directions.  Whenever
you see a theory that proposes different x- y- and z-pressures,
you know the theory is dead on arrival.

===============================

Extra credit:
  What do you say to the guy who went beyond
  his grazing area?