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Math in the News: 6/13/11

Date post: 26-Jun-2015
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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, while others have gently flowing streams of lava? Let's do the math! For more math resources, go to http://www.media4math.com.
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Page 1: Math in the News: 6/13/11

6/13/11

Page 2: Math in the News: 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.

Page 3: Math in the News: 6/13/11

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

Page 4: Math in the News: 6/13/11

Volcanic Eruptions

• This is the same type of volcanic eruption that covered the city of Pompeii in ash thousands of years ago.

• For a brief video on Pompei, click here.

Ash cloud

Page 5: Math in the News: 6/13/11

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?

Page 6: Math in the News: 6/13/11

Volcanic Eruptions

• 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.

Plinian eruption

Hawaiian eruption

Page 7: Math in the News: 6/13/11

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.

Page 8: Math in the News: 6/13/11

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.

Page 9: Math in the News: 6/13/11

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.

Page 10: Math in the News: 6/13/11

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.

Page 11: Math in the News: 6/13/11

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.

Page 12: Math in the News: 6/13/11

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.

Page 13: Math in the News: 6/13/11

Volcanic Eruptions

Lava Viscosity• Liquids that flow easily

have a low viscosity, and those that flow more slowly have a high viscosity.

Page 14: Math in the News: 6/13/11

Volcanic Eruptions

• 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.

Plinian eruption

Hawaiian eruption

Lava Viscosity

Page 15: Math in the News: 6/13/11

Volcanic Eruptions

• 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.

Lava Viscosity

Page 16: Math in the News: 6/13/11

Volcanic Eruptions

• 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.

Lava Viscosity

Page 17: Math in the News: 6/13/11

Volcanic Eruptions

• 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.

Lava Viscosity


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