Re: [Phys-l] question about Bernoulli

[John Denker <jsd@av8n.com>]

On 11/27/2010 11:37 PM, William Robertson wrote:

> Maybe people misunderstand what I'm looking for. The conversation  
> below gets halfway there. My comments interspersed.


On 11/23/2010 08:27 AM, LaMontagne, Bob wrote:

> > > the component of velocity of the molecules perpendicular to the
> > > pipe walls - was it reduced?

On Nov 23, 2010, at 9:22 AM, John Denker wrote:

> > Yes.

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

> This is a major step. Certainly if the component of velocity of the  
> molecules perpendicular to the pipe walls is reduced, that would  
> explain a lower pressure. Any lay person paying attention could  
> understand that. It makes sense ......

OK.

> It makes sense because if all we concentrate on in  
> the Bernoulli equation is pressure and velocity, we must assume that  
> height and density are constant.

I don't think we "must" assume that.  It's not true, and as
saying goes, it's bad luck to assume things that aren't true.

*) The density is never constant (in nontrivial cases).  The equation
of state makes it clear that you can't change the pressure without
changing the density.

*) The height may or may not be constant.
 -- In a wide range of practical application (such as carburetors,
  airplane wings, and Pitot/static gauges) the height-related terms 
  are too small to be interesting.
 -- In other cases, it is straightforward to rephrase the question
  so that the height-related terms drop out exactly.
 -- Failing that, it is straightforward to include the height-
  related terms in the equation, as John M. has done on occasion.

*) The temperature isn't constant either.

=========

I've seen some students who think there is an unwritten rule that
all variables not mentioned "must be" constant.  This is alas quite
wrong.  In real-world problems, innumerably many variables are not
mentioned, and few if any of the interesting variables are constant.
  http://www.av8n.com/physics/gas-laws.htm#sec-otbe