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Homework Help: How does the pressure vary as we go deep into the mines

  1. May 20, 2006 #1
    Sir,
    How does the pressure vary as we go deep into the mines and as move up into the atmosphere? I think as we move up into the atmosphere the pressure decreases. I am not sure.
     
  2. jcsd
  3. May 20, 2006 #2
    You can derive this yourself by considering the forces on a column of air in equilibrium.

    For a liquid, the relationship is too familiar, [itex]P(h) = P_{atm} + \rho g h[/itex] where h is the depth below the free surface at which the pressure is atmospheric. Note that this equation holds only if the density [itex]\rho[/itex] is constant. This too can be derived as above.

    Show your work here if you need more help.
     
    Last edited: May 20, 2006
  4. May 20, 2006 #3

    Hootenanny

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    One can estimate the pressure at a certain height above the ground using the exponential relationship;

    [tex]P_{h} \approx P_{0}e^{-\frac{mg}{kT}}[/tex]

    This is not entirely accurate as it does not take into account the changes in temperature which will occur. Therefore, this equation will give an overestimate of the pressure.

    Also, I would like to inquire as why you title all your post Heat?

    ~H
     
    Last edited: May 20, 2006
  5. May 20, 2006 #4
    You are right about the atmosphere. In general how pressure varies with height (or depth) in a fluid depends on how density varies. I can't say much about a mine. Are you asking how pressure changes as you below the earth's surface?

    EDIT: Sorry this post was written before I saw Hootenanny's reply.
     
  6. May 20, 2006 #5
    Sir,
    This expression given by you i.e. P(h) = P(o)e^(-mg/kT) doesn't have a direct dependence on h. Is the pressure indirectly related to h through g(acceleration due to gravity)?
     
  7. May 20, 2006 #6

    Hootenanny

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    My apologies Sir, it was a typo mistake on my part, the formula should read;

    [tex]P_{h} \approx P_{0}e^{-\frac{mgh}{kT}}[/tex]

    Apologies for any inconvience. I am still interested however as to why this thread is entiled 'Heat'

    ~H
     
  8. May 20, 2006 #7
    Sir,
    I feel that Pressure, Volume and temperature are terms closely related to Heat. So whenever my doubts involve these terms I give them the title heat. I think its troubling you a lot. Next time I will try to give a different title.
     
  9. May 20, 2006 #8
    Is the above mentioned expression applicable to pressure variation below the earth's surface also?
     
  10. May 20, 2006 #9

    Hootenanny

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    You are right, they are inseparable. The title doesn't bother me it was just I noticed that you were posting alot of Heat titled threads. I would just like to point out that you may get faster and more applicable responses if you had a more informative title. For example, one could entitle this thread 'Pressure dependence and height'. It is not a critisism and please do not take it as such, it is only a suggestion.

    ~H
     
  11. May 20, 2006 #10

    Hootenanny

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    I'm afraid not, the difference between predicted values and actual values become significant below the earth's surface.

    ~H
     
  12. May 20, 2006 #11
    Sir,
    Actually I never thought about it. I will surely take your suggestions in the right spirit. Next time I will try to be more specific in giving titles.
     
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