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Fluid Mechanics dimensional analysis repeating parameters

  1. Jun 4, 2017 #1
    This is more of a concept question; if I choose different repeating parameters to someone else, say my lecturer, and got different pi groups to him/her, however my groups are still dimensionless (i.e. the units for each pi group cancel to 1), is my answer still correct?
     
  2. jcsd
  3. Jun 4, 2017 #2
    This is more of a concept answer. Dimensional analysis looks as an elaborated science but actually it is just a trivial section of the vector algebra. Consider for example classical mechanics. All quantities have dimensions of the type ##L^{x}M^{y}T^{z}##. You can multiply quantities with dimensions ##L^{x}M^{y}T^{z}## and ##L^{x'}M^{y'}T^{z'}## to obtain a quantity with dimension ##L^{x+x'}M^{y+y'}T^{z+z'}##. You also can take a power ##\gamma## of quantity with dimension ##L^{x}M^{y}T^{z}## to obtain ##L^{\gamma x}M^{\gamma y}T^{\gamma z}##
    So we have a liner isomorphism ##L^{x}M^{y}T^{z}\leftrightarrow (x,y,z)\in\mathbb{Q}^3##. All other problems of the Dimensional analysis are easy reformulated and solved in terms of geometry of the vector space ##\mathbb{Q}^3##
     
  4. Jun 4, 2017 #3
    Let's see the details.
     
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