Math 95 #5851 Tues./Thurs 5:30 – 7:40 By Gina F. Blanchet-Parker May 31, 2011
• 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. • 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.
The cross-section of a cone geyser. (National Park Service, 2004.)
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 ofthe eruption until the last small splash above the cone at the very end.
A long eruption depletes more water from Old Faithful’s reservoir/sthan a short eruption does. It takes more time to refill thereservoir/s after a longer eruption than a shorter one.The physical properties of the geyser suggest a relationship betweenthe duration of an eruption and the time until its next eruption.Such a relationship may be exploited to predict times of eruptionfor a geyser.Note: Old Faithful has two reservoirs. A large and a small one. One or both of themerupt, thus it creates a long or a short eruption time.
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
90Time 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