Max Height of Ocean Island Volcanoes - A&B

[hfenton]

Homework Statement

Heights of volcanoes. You can assume that the density of basaltic magma is 2750 kgm-3, the density of lithospheric mantle is 3270 kgm-3, the density of oceanic crust is 2800 kgm-3, the density of seawater is 1030 kgm-3, and the depth of the ocean is 5 km.

A)What is the maximum height above the sea floor of an ocean island volcano fed by a magma chamber at the base of oceanic crust? Oceanic crust is typically ~7 km thick.

B)What is the maximum height above the sea floor of an ocean island volcano fed by a magma chamber at the base of oceanic lithosphere? Assume that the oceanic lithosphere is ~120 km thick.

Homework Equations

h = [(p(crust) - p( magma)) / p(magma)] * depth

The Attempt at a Solution

For A) [(2800-2750)/2750]*5000 = 90.91 m

For B) [(3270-2750)/2750]*5000 = 945.45 m

I don't think these are correct, because I don't know where I am supposed to use the density of sea water and the thickness of the oceanic crust and oceanic lithosphere. Any help would be greatly appreciated! Thanks!

 

[nate808]

Hello, thank you for your question. Your attempt at a solution is partially correct, but there are a few things that need to be adjusted.

Firstly, for A) you have correctly used the density of the oceanic crust and the magma to calculate the height. However, you do not need to take into account the density of seawater or the depth of the ocean, as these values are already accounted for in the thickness of the oceanic crust (which is given as 7 km). So the correct calculation would be:

h = [(2800-2750)/2750]*7000 = 254.55 m

For B), you need to use the thickness of the oceanic lithosphere (120 km) instead of the oceanic crust, as the magma chamber is located at the base of the lithosphere. Additionally, you also need to take into account the density of the lithospheric mantle, as this is the layer that the magma chamber is located in. So the correct calculation would be:

h = [(3270-2750)/2750]*120000 = 4363.64 m

I hope this helps clarify things for you. Keep up the good work!

 

[Blueshift5]

Your attempts at solving the problem are a good start. However, you are correct in questioning the use of the density of seawater and the thickness of the oceanic crust and lithosphere. These values are not needed to solve for the maximum height of ocean island volcanoes.

To find the maximum height of an ocean island volcano, we need to consider the densities of the materials above and below the magma chamber, which in this case are the oceanic crust and lithospheric mantle. The equation you used is a simplified version of the more complex equation for buoyancy, which takes into account the densities of all the materials involved.

So for A), the correct equation would be:

h = [(p(lithosphere) - p(magma)) / p(magma)] * depth

= [(3270-2750)/2750]*5000 = 945.45 m

And for B), the equation would be:

h = [(p(crust) - p(magma)) / p(magma)] * depth

= [(2800-2750)/2750]*120000 = 4363.64 m

These calculations assume that the magma chamber is located at the base of the oceanic crust or lithosphere and that the density of the magma is the same as the density of basaltic magma (2750 kgm-3). Keep in mind that these are theoretical maximum heights and in reality, the height of an ocean island volcano may be lower due to factors such as erosion.