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Dimensional Analysis

  1. May 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi. I have a function that contains 4 variables: Q, R, [itex]\mu[/itex], dp/dx

    I wish to choose 3 of them, such that they cannot be combined into a dimensionless product.


    I have chosen (correctly) R, [itex]\mu[/itex], dp/dx and I would like to know if my method sounds correct:

    If we know the dimensions: [R]=[L] [[itex]\mu[/itex]]=[ML-2T-2] and [dp/dx]=[ML-1T-1]


    and I know that in order for them to be dimensionless, their power product must equal zero:

    [L]a[ML-1T-1]b[ML-2T-2]c=[MLT]0

    or the system

    a-b-2c=0
    b+c=0
    -b-2c=0

    By inspection, this system can only be satisfied if a=0 but that does not make any sense since R is a physical quantity.

    Hence I have reasoned that these 3 variable cannot form a non-dimensional parameter by themselves.


    Does this work? Thanks!
     
  2. jcsd
  3. May 30, 2009 #2

    Pengwuino

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    Gold Member

    Ignore length real quick. [tex][MT^{ - 1} ]^a [MT^{ - 2} ]^b [/tex] can NEVER be dimensionless (except for a=b=0)
     
  4. May 30, 2009 #3
    Okay cool!

    Also, though longer and more tiresome, my method above works right? For the same reason.

    I just want a general method just in case inspection is not that obvious.
     
  5. May 30, 2009 #4

    Pengwuino

    User Avatar
    Gold Member

    Yes, that method works.
     
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