Re: [Phys-l] question about Bernoulli

[John Denker <jsd@av8n.com>]

On 11/23/2010 04:58 PM, LaMontagne, Bob wrote:
> iabatic, then pressure and density have to change in the same
> direction - so it's kind of chicken and egg. On the microsopic level,
> why does the density lower? Mass continuity requires rho*A*v to be
> constant in equilibrium flow, so small A will require higher v - but
> why a rho change? - it's not needed with a liquid obviously - so why
> with gas molecules with lots of space between them?
>
> If the gas molecules speed up, they must have suffered more
> collisions from the direction of the wider pipe and fewer from the
> direction of the narrower pipe - so we're back around the circle
> again.

If you insist on asking "why" then the laws of physics are
always going to lead you around the chicken-and-egg circle.
The laws of physics need to say what happens.  They sometimes
say how it happens.  The fundamental laws rarely if ever say
why it happens.  This is important.  This is what sets physics
apart from metaphysics and philosophy.  This has been called
Galileo's more important contribution, and has been called the
epoch, i.e. Day One of modern science.

The slightly different question "how do we know" will get a 
lot more traction.

In the case of a fluid flowing from a big pipe into a little
pipe, we know it *must* speed up because we know about
continuity.

Note that this "cause" is the cause of the knowing, not the 
cause of the speeding up.  We can perfectly well infer the
speed from the diameter *or* infer the diameter from the
speed (in this context).