1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Speeds inside tornado

  1. Jun 12, 2013 #1
    1. The problem statement, all variables and given/known data
    I am currently stuck on parts 2b,c and d of this problem.
    http://www.wopho.org/download/Theoretical_3_Tornado.pdf

    2. Relevant equations



    3. The attempt at a solution
    For part 2b, I use the the equation from part 2a and just integrate. I know that as we exit the tornado, the pressure should be atmospheric pressure so I can solve for the constant. but the problem that I have is the ln(r) term. I can choose a sufficiently small r such that the pressure is negative which does not make sense.

    2c) I'm assuming it related to part 2b) so I have left that out for now.

    For part 2d) I think that the solution would involve something about the dew point in air but when I type for information regarding the dew point into Google, I just get complicated formulae. Could someone perhaps suggest a website where I can get more information about this.

    Any help would be appreciated.
     
  2. jcsd
  3. Jun 12, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Since v = v(r), I don't understand how you can "just integrate" that equation. Seems to me you need another equation from somewhere. E.g. if we assume irrotational flow except at the centre, v ~ 1/r; or if we treat it as rigid body, v ~ r. Either way, the DE gives you a formula for P=P(r), and doesn't seem to contradict any given info. Maybe I'm missing something.
    Oh, and please post your working.
     
  4. Jun 13, 2013 #3
    For my working, P=∫ρairv2/r dr and then I got a ln(r) term which I can now see is wrong. For a later part (3b inside the tornado) they assume that it is a rigid body so so v~r. Would it be sensible to assume irrotational flow and what other things exhibit this kind of flow? Also, would the method then become:

    v=k/r
    dP=ρairk2/r3dr
    Now I integrate and use the contidion that when r=rc, v=vc to solve for k. Then I use that as P=Patm as r→∞ to eliminate the constant of integration.
     
  5. Jun 13, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The standard treatment of a vortex is that it is irrotational flow, except in a core region, where it is more like rigid body. See http://en.wikipedia.org/wiki/Vortex. I was not at all sure which you were expected to use, or maybe some fancier relationship that encompasses both.
    Looks right.
     
  6. Jun 18, 2013 #5
    Thanks for your help. I have been researching the tornado and wikipedia says the water condense due to adiabatic cooling. I know that means P1-γTγ=constant and they also give γ suggesting this is perhaps the correct approach to part d). I understand that with the equation for pressure, i need to equate this to the pressure at which water condenses but how can I do this?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted