From: mkagalen@lynx.dac.northeastern.edu (michael kagalenko)
Subject: Re: bubble in container
Organization: Northeastern University, Boston, MA. 02115, USA
Date: Sun, 27 Dec 1992 01:31:27 GMT

In article <1992Dec26.173915.16068@sfu.ca> Leigh Palmer <palmer@sfu.ca> writes:
>In article <1992Dec26.033119.5443@lynx.dac.northeastern.edu> michael 
>kagalenko, mkagalen@lynx.dac.northeastern.edu writes:
>
>>I can't bear a fealing of pity to the students of SFU, since all of the 
>>above is incorrect. If bubble of air is not accelerating, the pressure
>>does not depend on its position. (Doubts ? Recall conservation of the 
>>momentum from your "Physics 101" :) I'd like to point out that Arhimed
>>force on the bubble does not depend on its position as well, provided
>>liquid is incompressible & container abs. rigid
>
>Hmm... I'll try to relieve that "unbearable fealing" you're having. The 
>phenomenon, as I said, is counterintuitive. That is why physics is of 
>value; it replaces intuition when intuition fails us.
>
>First, note that the volume, V, of the bubble is constant throughout 
>this process. Thus, if the system is in thermal equilibrium at 
>temperature T*, the pressure, P, in the bubble will remain constant 
>throughout the process. This does not depend upon a particular model for 
>the gas in the bubble, but only upon the *existence* of an equation of 
>state P(V,T). You may think of it as an ideal gas, however, if you wish 
>to do so. The practical efficacy of this phenomenon depends upon the 
>bubble being very compressible, and a gas is a good choice.
>
>Second, note that the bubble now establishes a pressure in the fluid in 
>the horizontal plane of its location, since it is in hydrostatic 
>equilibrium with the fluid. Only the position of the bubble is necessary 
>to specify the elevation of this horizontal isobar.
>
>Third, consider the pressure at other points in the fluid in hydrostatic 
>equilibrium in a uniform gravitational field which are located a 
>distance z above the bubble. The pressure 
>
>                        P(z) = P - rho g z,
>
>where the symbols used are the same as before.
>
>By raising the altitude of the bubble, and consequently of the 
>(constant) P isobar, we decrease z everywhere in the fluid, thus 
>increasing the pressure correspondingly.
>
>Cute, eh? This mechanism, applied to bubbles in magma chambers closed at 
>their tops, has been proposed as the source of the tremendous pressures 
>associated with explosive volcanic eruptions. The energy which is seen 
>in such eruptions is not stored in the relatively incompressible magma, 
>but in the bubbles. The extreme pressures are necessary to rupture the 
>capsules in the first place, and the bubbles (mostly steam, I believe) 
>transport this energy to the surface by rising relatively isochorically. 
>in the magma chamber.
>
>This sort of counterintuitive phenomenon, when introduced to a class of 
>students at SFU, usually initiates a lively discussion rather than any 
>feeling of distress. I feel that students receive valuable exercise in 
>thinking when discussing such things. You need not pity them; they do 
>quite well. Last week one of our physics majors successfully defended 
>his physics PhD thesis at Princeton, and another did so at Cambridge. We 
>don't have results like that every week, but we do have a large number 
>of our undergraduates out in the world doing quite well for themselves.
>
>Leigh
>
>*This is an Ansatz I intentionally neglected to state in order to 
>heighten the sense of mystery by misdirection. You bit because you 
>thought it was a mechanics problem.

Hmm, I'd admit my mistake :) - my arguments mean that the difference 
between pressure on the top & on the bottom of container does not 
depend on the position of the bubble. As a little revenge, I'm posting 
one neat problem (which I solve when I was in the secondary school)

			      /\
			    /    \
			  /	   \
			/	     \
		      /		       \
                    /			 \
  		 ./________________________\.
                /|	      /\	    |\
              /	 |	    /	 \	    |  \
            /	 |	  /	   \	    |	 \
	  /	 |	/____________\	    |	   \
	/	 |    /	|	     | \    |	     \
A     /		 |  /	|  and so    |	 \  |	       \
___./		 |/	|  on to     |	   \|	         \.___ B 
    \		 |\	|  the	     |	   /|	         /
      \		 |  \	|  infinity  |	 /  |	       /
        \	 |    \	|____________| /    |	     /
	  \	 |	\	     /	    |      /
	    \    |	  \   	   /	    |    /
	      \	 |	    \	 /	    |  /
		\|____________\/____________|/
		  \	 	           /
		    \	 		 /
		      \		       /
			\ 	     /
 			  \	   / 
			    \    /
			      \/

This configuration is made of conductive wire which resistance is
proportional to the length. Let the resistanse of the biggest edge is
R ; what is the resistance between A & B ? (please, solutions by e-mail;
do not spoil the pleasure to the others ;-> ) 
Enjoy !