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Confusion on wording of a dimension problem

  1. Jan 21, 2013 #1
    the speed v of sound waves in a gas can be express in terms of the pressure p and the density q (mass per unit volume) of the gas, as v=ap^bq^c, where a, b, and c are dimensionless constants. The dimensions of pressure are m/((LT)^2). What must be the values of b and c.

    I am confused on what to write for the dimensions of q. Would it be m/L^3 as in mass/volume?
     
  2. jcsd
  3. Jan 21, 2013 #2

    berkeman

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    Staff: Mentor

    Welcome to the PF.

    Could you add some parenthesis to your equation to eliminate the ambiguities?

    "v=ap^bq^c"
     
  4. Jan 21, 2013 #3
    v=a(p^b)(q^c)
     
  5. Jan 21, 2013 #4

    berkeman

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    Staff: Mentor

    Ah, that helps. Now can you fill in the units for each term? I usually use square brackets to indicate the units like v[m/s].
     
  6. Jan 21, 2013 #5
    v=[L/T], p=[M]/[L][T^2]
     
  7. Jan 21, 2013 #6
    Read up on the Buckingham Pi Theorem. That is what is involved here.

    Chet
     
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