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Dimensional analysis

  1. Feb 15, 2012 #1
    The velocity of waves in a liquid depends on the wavelength λ, surface tension γ, and density ρ, of the liquid, Derive an equation to relate v, with wavelength, surface tension and density, (note: surface tension, has a formula of force per unlit length and SI unit of Nm^-1)
     
  2. jcsd
  3. Feb 16, 2012 #2

    PeterO

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    reducing to fundamental units

    λ - m
    γ - N.m-1 = kg.m.s-2.m-1 = kg.s-2
    ρ - kg.m-3

    The final answer is velocity, so m.s-1

    If you multiply all three together [ie λ x γ x ρ] we have m x kg.s-2 x kg.m-3 = kg2.s-2.m-2

    Not quite what we wanted. We needed the kg to cancel out, so one of γ or ρ needed to be in the denominator.

    The fact that all units were squared doesn't matter - we can throw in a √ at the end to fix that.

    have a play round and see how you get on.
     
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