# What units will this equation have?

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1. Oct 21, 2015

### RyanUSF

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. Oct 21, 2015

### RyanUSF

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?

3. Oct 21, 2015

### pasmith

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