Re: [Phys-l] question about Bernoulli

[William Robertson <wrobert9@ix.netcom.com>]

I've been away from this conversation for a few days, so I have  
catching up to do. In skimming, I have noticed a concern for the need  
for a molecular explanation of Bernoulli. That concern includes moving  
in too big a leap from the macro to the micro. A picture of what the  
molecules are doing is not always necessary, or perhaps not always  
possible, especially when discussing large-scale results of large  
numbers of molecules. But when we can get that picture, it certainly  
helps with understanding.

If I might give a more basic example. We learn gas laws as they have  
arisen historically, or simply as the ideal gas law PV=nRT or PV=NkT.  
One can address the gas laws at this level, as interactions between  
pressure, volume, temperature, and number of molecules or moles. But  
is it possible to gain a deeper understanding, one that stays with  
students (of all ages) because it provides a concrete picture of  
what's going on? Absolutely. I do a simulation with teachers in which  
they pretend to be gas molecules with others being their container.  
They are given a few simple rules about interaction. Once they have  
those rules, they can "experience" the gas laws. Increased temperature  
means they move faster. What does this do to the pressure (how often  
and how hard the molecules hit their container)? Does this mean the  
gas as a whole expands? No, unless the container "gives" (ask the  
average elementary or middle school science teacher whether a gas  
expands or not when you heat it). What happens to the pressure when  
you change the number of molecules (add or subtract people from the  
"container") or change the size of the container? It's obvious in the  
people simulation. Do molecules "need more space" when you heat them  
(a common incorrect explanation in resources)? The answer is obvious  
in the people simulation. As you make the simulation more  
sophisticated, you can demonstrate the physical effect on a gas when  
it does work on the container or vice versa.

Such a simulation is extremely helpful in understanding the ideal gas  
law. In fact, if one does this prior to ever introducing the math of  
the law, the law makes conceptual sense and isn't that scary for those  
(many!) who freak out at the first sight of an equals sign. The major  
concern in such a simulation is that we not introduce any  
misconceptions regarding how gases behave.

It's in the spirit of the simulation I describe that I asked the  
question regarding Bernoulli. Is it possible to understand the  
Bernoulli effect in terms of molecular motion and changes in molecular  
motion on a level that makes the effect "obvious" once one pictures  
what the molecules are doing? Until I get through everything in this  
thread, I don't yet know the answer to that question. It might very  
well be my job to use what all have generously provided, come up with  
what I think is a proper molecular "picture," and run it by the group.  
I do hope I have explained why I asked the question in the first place.


Bill




On Nov 24, 2010, at 4:33 PM, LaMontagne, Bob wrote:

> Again, there is no argument from me about the physics of the flow in  
> terms of pressure, density, temperature, etc., as covered by the  
> Bernoulli equation.
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