[Geysers] Constrictions, bubbles, and pressure

[Ron Keam]

Jeff's experiment is interesting.  Here are some 
comments which I hope will throw light on his 
observations.  They do not provide a complete 
answer, but I have indicated the source of the 
physical effects that are ignored in the simple 
approximation described below.

With the unrestricted tube one presumably has a 
uniform horizontal cross-section.  The bubble 
will contain a fixed amount of air.  Because the 
depths at which the bubble movements are being 
considered will be over a fairly restricted 
range, one can assume that its volume changes are 
negligible.  Therefore its vertical extension 
will be approximately constant.   Let that 
constant extension be ß. If the bubble is on side 
A of the U-tube, and the other side is B then the 
level of water surface near the top of A will be 
precisely ß higher than the level of the water 
surface near the top of B. (Just use equality of 
rho. g.h on both sides down to the bottom of the 
U-tube.)  When the bubble is passing through the 
constriction its average cross-section is 
reduced.  Therefore, to keep its volume constant 
its vertical extension must become greater than 
ß.  Thus the difference in level between the free 
water surfaces in A and B must also increase. 
This does not say whether the surface on side A 
rises or the surface on side B falls.  Evidently 
from Jeff's observation it is the latter that is 
seen.  Once the bubble has passed through the 
constriction the bubble resumes its vertical 
extension ß and so also does the difference in 
the level in A and the level in B.

NOTE:  I have used an argument based on assuming 
at each stage that static pressure gradients 
apply.  That ignores dynamic effects, and it is 
they that will determine the actual observed 
result - i.e. that it is that side B water level 
decreases rather than side A rises (or that it is 
some of both).

Ron Keam

>Here is an interesting experiment.  I believe it shows that when a bubble
>rises through a constriction in
>a geyser system, the pressure drops briefly.  If the pressure drops, the
>boiling rate should increase, and
>this might trigger an eruption.
>
>1) Obtain 4 feet of tygon tubing, surgical tubing, or similar material.
>2) Fill it with water.
>3) Get a bubble situated in the middle of the tubing section.
>4) Now hold both ends open, vertical, and next to each other.  The bubble will
>rise up one side of the U
>tube.
>5) The water level in the side containing the bubble will be highest.
>6) Pinch the tubing above the bubble so that the bubble must flow through the
>constriction on its way
>to the surface.
>7) Note that the water levels change while the bubble is flowing through the
>constriction.  The low side
>gets lower, but it rebounds once the bubble has passed through.
>
>I suspect this last observation means that the pressure dropped while the
>bubble moved through the
>constriction.  Why this happens isn't clear to me.
>
>I welcome explanations.
>
>I must get back to doing something productive.
>
>Have fun.
>
>Jeff Cross
>jacross at lamar.colostate.edu
>
>
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Ron Keam
The Physics Department
The University of Auckland
Private Bag 92-019
Auckland
New Zealand
Phone +64 9 373-7599 extension 87931
FAX +64 9 373-7445
EMail r.keam at auckland.ac.nz
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