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What units will this equation have?

  1. Oct 21, 2015 #1
    Let u be density of something (heat, smell, etc.). Assume the something only diffuses; there’s no convection or ballistic transport. Let’s work in one spatial dimension (x). Then u satisfies the diffusion equation,

    ∂u/∂t = D ((∂^2)u/(dx^2))
     
  2. jcsd
  3. Oct 21, 2015 #2
    would separating the equation such that D = (∂u/∂t)((∂x^2)/(d^2u)) be of any help? Would the spatial dimensions cancel eacher out just giving dx^2/dt so units of m^2/s?
     
  4. Oct 21, 2015 #3

    pasmith

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    Both sides have dimensions of [itex](\mbox{something density}) T^{-1}[/itex]. Diffusivities always have dimensions of [itex]L^2 T^{-1}[/itex].
     
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