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Showing the Terminal Velocity equation is dimensionally correct.

  1. Mar 2, 2012 #1
    Hey guys, this is my er...first post.
    It's a first year university physics assignment that I'm having a bit of trouble with, any help will be rewarded with kind words!(bit of an empty gift, but it's all I have)

    Ok, here's the problem.

    The terminal velocity of a mass m, moving at ‘high speeds’ through a fluid of density ρ (kg m^3), is given by
    V(terminal)=√((2mg)/(DρA))

    where A is the cross-sectional area of the object (m2) and D is a dimensionless “drag coefficient”.
    Show that equation is dimensionally correct.

    Now, not really being certain what the question is asking for regards 'dimensions' hasn't helped but! I did make an attempt by substituting each variable with it's corresponding units.
    e.g.

    2mg= 2((m/s^2)x(kg))=((m x kg)/ s^2)and ρA=((Kg/m^3)x(m^2))=Kg x m^(-1)

    which yields V(ter)=√((mKg)/ s^2)/mKg
    =√(s^2) x D
    =s x D

    This seems more or less nonsensical.
    I'm sure it's probably mathematical error or just a failure to grasp the concept of proving an equations dimensions.

    Am I wrong?
    what is going on?
     
  2. jcsd
  3. Mar 2, 2012 #2

    vela

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    Problems from introductory courses don't belong in the advanced physics homework forum. I moved your thread.

    Fine up to here. Your dimensions for ρA are therefore kg/m, right?

    You used kg m instead of kg/m for the dimensions of ρA.

     
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