This document discusses geysers and how to predict the eruption schedule of Old Faithful geyser. It explains that geysers consist of a reservoir, opening, heat source, and underground channels. Eruptions occur when water in the reservoir becomes so hot it expands into steam. This triggers a chain reaction that ejects water and steam through the opening. After eruptions, the reservoir refills until the next eruption. The document also presents a linear equation and data showing the relationship between the duration of an eruption and the time until the next eruption for Old Faithful geyser. Predicting eruptions is possible based on this relationship between duration and refill time.

1. Math 95 #5851 Tues./Thurs 5:30 – 7:40
By Gina F. Blanchet-Parker
May 31, 2011

4. • A geyser is a natural phenomenon: a type of hot spring which shoots water and steam
into the air.
• Every geyser consists of a reservoir for water storage, an opening through which steam
and hot water can be released, a heat source, and underground channels to replenish
the water supply after an eruption.
• A geyser erupts when some of the water in its reservoir becomes so hot that the
expansion of the water into steam becomes more than the reservoir can handle.
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• This triggers a chain reaction with the other water in the reservoir and eventually a bit
of the super-hot water from the reservoir escapes to the surface and explodes into
steam.
• This initial explosion then triggers the rest of the water in the reservoir, some or all of
which is ejected through the opening in further eruptions.
• After the eruptions have ended, the reservoir again fills with water, and the process
repeats itself.

5. The cross-section of a cone geyser. (National Park Service, 2004.)

6. Yes, it is possible to predict the next eruption of Old Faithful, but
not more than one eruption in advance. The time until the next
eruption depends upon the duration of the previous eruption .
To predict the eruption schedule of Old Faithful I used the
following linear equation: T = 12 L + 34
T = Time Until Next Eruption
L = Duration* of Previous Eruption
•The duration is timed from the first heavy surge which lifts water skyward at the start of
the eruption until the last small splash above the cone at the very end.

7. A long eruption depletes more water from Old Faithful’s reservoir/s
than a short eruption does. It takes more time to refill the
reservoir/s after a longer eruption than a shorter one.
The physical properties of the geyser suggest a relationship between
the duration of an eruption and the time until its next eruption.
Such a relationship may be exploited to predict times of eruption
for a geyser.
Note: Old Faithful has two reservoirs. A large and a small one. One or both of them
erupt, thus it creates a long or a short eruption time.

8. Duration* of Eruption Time Until Next Eruption
(minutes) (+/- 10 minutes)
1.5 52
2.0 58
2.5 64
3.0 70
3.5 76
4.0 82
4.5 88
5.0 94

9. 90
Time Before Next Eruption in 80
70
60
Minutes
50
40
30
20
10
0
1.5 2 2.5 3 3.5 4
Length of Prior Eruption in Minutes