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Dimensional Analysis homogeneous

  1. Sep 24, 2011 #1
    Determine which of the following equations are dimensionally homogeneous. Show
    your work



    ΔP/Q = 17L(μ)/(w^4)


    where ΔP is the pressure drop in a channel of triangular cross-section, Q is the
    volumetric flowrate, L is the channel length, μ is the fluid viscosity, and 2w is the
    length of one side of the triangle


    i have

    ΔP = F/A = ML(T^-2)
    Q = volume/seconds = (L^3)/T

    so...

    ΔP/Q = M(T^-1)(L^-4)

    For the other side of the equation I do not know how to deal with fluid viscosity and do I ignore the 17?
     
    Last edited: Sep 24, 2011
  2. jcsd
  3. Sep 25, 2011 #2

    lewando

    User Avatar
    Gold Member

    The viscosity, μ, has units of Pa⋅s, or (N⋅s)/m2, or kg/(m⋅s). Yes, ignore the unitless constant 17.

    does not look right.
     
  4. Sep 25, 2011 #3
    Thank you so much I have spotted the problem
     
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