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# Math in the News: 6/13/11

## by Media4math on Jun 12, 2011

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In this issue of Math in the News, we look at volcanic eruptions in light of the recent eruption of the Chilean volcano, Puyehue. Why do some volcanoes spew out hot ash thousands of feet in the air, ...

In this issue of Math in the News, we look at volcanic eruptions in light of the recent eruption of the Chilean volcano, Puyehue. Why do some volcanoes spew out hot ash thousands of feet in the air, while others have gently flowing streams of lava? Let's do the math!

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## Math in the News: 6/13/11Presentation Transcript

• 6/13/11
• Volcanic Eruptions
The Puyehue eruption sent an enormous cloud of ash into the sky.
For some dramatic footage of the eruption, click on this video link.
• Volcanic Eruptions
This satellite image shows that the ash cloud from the eruption rises above the normal cloud layer.
This means that the ash rose thousands of feet into the air!
Ash cloud
• Volcanic Eruptions
This is the same type of volcanic eruption that covered the city of Pompeii in ash thousands of years ago.
Ash cloud
• Volcanic Eruptions
Communities that are located near volcanoes are at some risk, but it is slight. Volcanoes erupt very infrequently. But volcanic soils near volcanoes are often very fertile farmland, so there is an economic reason for living near volcanoes.
Activity: How could you measure the probability of a volcano erupting?
• Volcanic Eruptions
Plinian eruption
Not all volcanoes are as violent as Puyehue. In fact, volcanoes in Hawaii don’t eject ash thousands of feet in the air; instead, they spew steady streams of lava.
For an example of a freely flowing Hawaiian eruption, click on this video link.
Hawaiian eruption
• Volcanic Eruptions
In both cases, lava is flowing through an opening in the Earth, usually through what is termed a lava tube.
Think of a lava tube as a cylinder through which a liquid––lava––flows.
• Volcanic Eruptions
Lava Viscosity
As lava flows through the lava tube, you might assume that the cylinder flows through the tube like a bullet through the chamber of a gun.
But lava is a fluid, and a cylinder of fluid has a different type of movement.
• Volcanic Eruptions
Lava Viscosity
The part of the lava that comes in contact with the lava tube is slowed down due to friction. This part of the cylinder travels at a slower speed than the interior cylinder of lava.
• Volcanic Eruptions
Lava Viscosity
The slowing down of cylinders of lava continues through the center of the lava flow. This diagram shows that the inner cylinder of the lava is moving at a faster speed than the other concentric lava.
• Volcanic Eruptions
Lava Viscosity
The velocity within the lava flow varies. The diagram shows the velocity at any radius, x, given maximum velocity, vm, and maximum radius, R.
• Volcanic Eruptions
Lava Viscosity
The graph of the function v(x) shows a parabola. The maximum velocity is at the center of the lava flow. The velocity is zero where the lava meets the wall of the lava tube.
• Volcanic Eruptions
Lava Viscosity
Liquids that flow easily have a low viscosity, and those that flow more slowly have a high viscosity.
• Volcanic Eruptions
Lava Viscosity
Plinian eruption
Volcanic eruptions that result in huge plumes of ash have high-viscosity lava.
Volcanic eruptions that result in streams of flowing lava have low-viscosity lava.
Hawaiian eruption
• Volcanic Eruptions
Lava Viscosity
Try this experiment with a bottle of glue. In the first scenario model a low viscosity volcano. In the second, model a high-viscosity volcano.
• Volcanic Eruptions
Lava Viscosity
High-viscosity lava flows slowly and pressure builds up within the lava tube. As the pressure increases, the top of the volcano explodes with smoke and ash and the ejected material can reach thousands of feet in the air.
• Volcanic Eruptions
Lava Viscosity
But highly viscous lavas aren’t just a little bit more viscous. This graph shows the massive exponential difference between the Hawaiian-style lavas and the lava from Puyehue-style lavas.