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Math Help - weber number - dimensional analysis

  1. #1
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    Question weber number - dimensional analysis

    can someone check this for me?


    weber number = density*velocity^2*length/surface tension

    find dimensions of surface tension.

    density= ML-3
    speed = [LT-1]^2
    Length = L

    so

    [ML^-3]*[LT^-1]^2*[L]

    = MLT

    So for weber number to be dimensionless the surface tension has to cancel out MLT and therefore also has dimensions MLT.
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  2. #2
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    Quote Originally Posted by thermalwarrior View Post
    can someone check this for me?


    weber number = density*velocity^2*length/surface tension

    find dimensions of surface tension.

    density= ML-3
    speed = [LT-1]^2
    Length = L

    so

    [ML^-3]*[LT^-1]^2*[L]

    = MLT

    So for weber number to be dimensionless the surface tension has to cancel out MLT and therefore also has dimensions MLT.
     [ ML^{-3} ] [ L T^{-1} ]^2 [ L ]

    = [ M ] [ L^{-3} L^2 L ] [ T^{-2} ] = [M T^{-2} ]

    -Dan
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