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Finding values of constant by using Dimensional Analysis

  1. Jan 30, 2016 #1
    1. The problem statement, all variables and given/known data
    The speed v of sound in a gas depends on the density p and pressure P of the gass. If this dependence is in the form of a power law that is,

    v = kpaPb

    where k, a and b are constants (k a dimensionless one).
    a. Determine by dimensional analysis the values of a and b.
    b. There by rewrite the above equation in a simpler form.

    2. Relevant equations

    v = kpaPb

    3. The attempt at a solution

    I started off by writing the dimensions in the equation

    [L][T]-1 = ( [M][L]-3 )a ( [M][L]-1[T]-2 )b

    From here, i think i have to try and find the values for a and b that allows the right hand side of the equation to match the left. Also in this situation, do i just leave K out of it?
    Any help to proceed to next step towards the answer would be great.
     
  2. jcsd
  3. Jan 30, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Right.
    k is dimensionless, so it is irrelevant here.
     
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