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Using Airy's Model of isostatic equilibrium, solve for....

  1. Nov 3, 2015 #1
    1. The problem statement, all variables and given/known data
    Using Airy's Model of isostatic equilibrium, solve for the average anti-root height due to the ocean and the average density of the upper mantle.
    Airy_Isostasy.jpg

    given info: ocean depth avg = 4km
    ocean crust is 10 km thick avg
    continental crust if 40 km thick avg
    all crust is the same density (2.5g /cm3), density of water is (1g/cm3)
    [[[[We can't use the value given for the mantle density in the image]]]]


    2. Relevant equations
    0b493e743a92707e31d334bce2486fa5.png
    3af435626f6ddb3a296e5f24d2688f6d.png
    13a327cede7fab51b179bf2689314e69.png

    3. The attempt at a solution
    I know the equation to find the avg height of the anti-root, but you need the density of the mantle to solve for it..? This isnt given to us

    The next question is to solve for the density of the mantle, and from the equation manipulation ive done, you need the height of the anti root to solve for this?
    I feel like I'm missing something super obvious.

    Mantle density (gravity is left out because it appears in all terms)
    ρc = crust density, ρw = density water ρm = mantle density

    ρwh2 + ρc(C-h2-d2) + ρm(b2+b1) = ρcC + ρmb1
    ρwh2 + ρmb2 = ρch2 + ρcb2
    ρm = (ρcC + ρcb2 - ρwh2)/ b2

    you need b2 (the anti-root height) to solve this, and you need the ρm to solve for anti root height? I feel like I'm missing something very obvious????
     
  2. jcsd
  3. Nov 8, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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