May 24, 2009
Los Angeles, CA
July 14, 2009
Richmond, Indiana
IYPT 2008 #12: Geyser (Modified): Support a long, vertical tube in a vessel
containing water. Heat the vessel directly from the bottom and you will observe that
the water erupts. Arrange for the water to drain back into the vessel to allow
repeated eruptions. Investigate the parameters that determine the eruption
frequency.
References and Introductory Cooments:
Geyser is a "well-known" phenomenon and many science museums and science
departments show demonstration of geysers. The body of literature on the physics of
geysers is surprisingly sparse, which makes this a good YPT problem. However, you
will not be able to open just one source and have a problem solution.
1. Rinehart, J. S., “Old Faithful Geyser,” Physics Teacher, 7, (April 1969) pp. 221-224.
This is an old article that spends most of its time discussing the Old Faithful geyser at
Yellowstone National Park. He does show actual frequency data for the eruptions over a
period of years and one can "see" that "Old Faithful" isn't quite as regular is its nickname
might imply. Rinehart does put in some important physics for the problem when
describes the temperature behavior at a depth of 30 meters and shows how the
phenomenon of boiling point elevation due to the rise of hydrostatic pressure affects
formation of geysers. Adapting and explaining that to your students will not be trivial but
will be important.
2. Lienhard, John H. IV and Lienhard, John H. V A Heat Transfer Textbook 3rd edition.
This fairly advanced text (junior to graduate level) is completely downloadable at
http://web.mit.edu/lienhard/www/ahtt.htm. It's a great text and we are indebted to this
father-son duo for taking a book that was a moderate commercial success in editions 1
and 2 and making it available to all on the web. The text focuses mostly on
incompressible fluids (i.e. water) and heat transfer. The later chapters on boiling are
particularly complete. The one chapter on compressible fluids (i.e. air or steam) and heat
transfer should get across the ideas that using the ideal gas law is not just a simple plug
and chug.
3. Any introductory text that covers fluids and heat transfer such as those by Sears and
Zemansky or Halliday and Resnick, etc. There are numerous engineering texts on the
market that go into enormous detail. Whenever you enter one of these be very very
careful to figure out if the author(s) is/are talking about compressible or incompressible
fluids. Geyser has both and this is one of the major challenges in this problem for the
teacher/advisor.
Guide:
1. Wording. So why did we modify the IYPT 2008 wording? Basically due to safety
and simplicity. The photo on our webpage was taken from the University of Illinois
demonstration page and it represents one type of geyser. This type has the erupting water
being collected in a large pan attached to the top of the eruption tube and the water drains
back down that tube to the heating reservoir. This rough model seems closer to natural
geysers than the following, but since neither of us have crawled down inside a natural
geyser we aren't sure. The other common type of geyser is a percolating coffee pot where
an inverted funnel is placed inside a pot full of water. The erupting water then falls down
to the heating reservoir outside the eruption tube but inside the pot.
Our wording permits either design and here's why. The issue here isn't closer
approximation to a natural geyser, but safety. Heating glass (so you can see what's
happening inside) containers filled with water needs to be done carefully. Chemistry
teachers and knowledgeable cooks can show almost any novice physics teacher why
chemists love Pyrex beakers – their wall thicknesses have been carefully formed so that
heating up to temperatures about water boiling produce few, if any, differential heat
stresses that break the vessel. One way to get into semi-trouble with this experiment is to
just blindly grab any interestingly shaped glass tube with a bulb on the end and heat it.
For the first time or two use goggles and a shield.
2. Experiment. You can observe eruption
using any setup that allows you to drain
water back in the tube, as we've discussed
above. The apparatus pictured to the right is
just a possible one that mimics those shown
in most science museums. A lower container
has a shape of a truncated cone narrower at
the top. A stopper connects it with a glass
pipe. The pipe is connected to an upper
container. A supports keeps parts stable.
There is a hot plate under the lower
container. After awhile….(it takes a long
time to get a large volume of water to boil
(good place to start some calculations with
your students and discuss various types of boiling) an eruption can occur. It will
probably take numerous "runs" to get repeated eruptions going with your apparatus.
3. Splashing vs Erupting. When water boils in a container with a cylindrical shape the
bubbles of steam make splashes when the bubbles erupt at or above water surface.
Splashes become stronger when water remains on a hot plate after it starts boiling. These
splashes form because of mechanism of boiling. At the temperature when vapor pressure
becomes higher than atmospheric pressure bubbles expand due to the intense evaporation
of water inside them. Buoyant force moves them up.
I use here word “splash” when I speak about water droplets that jump from the surface
continuously. I use word “eruption” to describe water jets that glass pipe shots
periodically. Eruption occurs when the container becomes narrow and bubble takes the
whole width of the container. When the bubble expands, it displaces water that is above
the bubble. This water erupts outside the container. Afterwards water drains back in the
container. Continuous splashes involve water in motion up and back simultaneously.
Eruption happens when water first moves up and than it drains back. You can observe
different development of eruptions by varying shape of your container and by using
different mechanisms of draining water back into container. Eruptions also differ
depending on temperature of the hot plate and water that drains back. Colder water can be
a reason of longer break between eruptions.
4. Modeling all of this. A complete model will have lots of parts – boiling the water in
the reservoir, bubble formation and movement to the water surface, interaction with the
conical surface of the inverted funnel, gas expansion doing work on the liquid water in
the tube, the liquid water's interaction with the tube the air above the steam below, etc
etc. Somewhere in there you need to predict a frequency and compare to your results.
Good Luck!
T.Bibilashvili
B. Oldaker