Re: [Phys-l] question about Bernoulli

[brian whatcott <betwys1@sbcglobal.net>]

You certainly know, as we all do, that moving a column of air down a 
pipe reduces the pressure
at the pipe wall, which implies the reduction of the kinetic energy in 
that direction, which implies lower normal velocity. At the same time, 
this moving air provides dynamic pressure in the flow direction
with higher axial energy.
That much is clear.
And conservation arguments lead to the need for maintenance of the sum 
of potential energy and kinetic energy constant.

But you wanted some plausible modality to explain these by no means 
obvious results.
I took some pleasure in finally drawing a diagram. It is unsuitable for 
student use,  or for too ready acceptance by academics for that matter. 
Still, you might have fun with it, as I did.
(two formats - a gif and a jpg with the same contents.)

http://i880.photobucket.com/albums/ac6/betwys/BD.gif
http://i880.photobucket.com/albums/ac6/betwys/BernoulliDepression.jpg

Brian W

On 11/18/2010 4:42 PM, William Robertson wrote:
> It seems that adding this component of velocity parallel to the pipe 
> does not affect the component of velocity perpendicular to the pipe. 
> You have a greater overall velocity, with the component perpendicular 
> to the pipe remaining as it was when the air was "still." And if you 
> are somehow reducing this perpendicular component of velocity, what is 
> the mechanism for that? Sorry if I'm being dense on this.
>
> Bill
>
>
> William C. Robertson, Ph.D.
>
>
> On Nov 17, 2010, at 6:02 PM, brian whatcott wrote:
>
> > How about this?
> >
> > Draw a circle of unit radius. The circle depicts the speed and 
> > direction of any air particle in the middle of a pipe.
> > Draw two parallel horizontal lines touching the circle, one on each 
> > side. The two straight lines represent a pipe.
> >
> > From the center of the circle, draw an arrow perpendicular to the top 
> > horizontal.
> > The perpendicular arrow represents the speed of one particle hitting 
> > the pipe, contributing some pressure, proportional to the arrow's 
> > length.
> >
> > Now draw a third short horizontal line with a arrow between the other 
> > two horizontal lines - representing the speed with which all the air 
> > is now moved.
> >
> > This 'wind' arrow will move any particle moving towards a wall.  The 
> > vertically moving particle now moves instead at a forward slant. So a 
> > particle with the SAME speed as before now has a forward component. 
> > The outward component of its speed is reduced for this reason....
> >
> > This argument cries out for a diagram, in the Newtonian manner!
> >
> > Brian W