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I am trying to get units working in mathematica in the following expression for diffusion:

$D = {K_B T}/{3 \pi \eta L}$

My code is as follows:

KB = Quantity[1.380650*10^-23, ("Meters")^2*"Kilograms"*("Seconds")^-2*("Kelvins")^-1];
T = Quantity[20 + 273.15, "Kelvins"];
eta0 = Quantity[8.9*10^-4, "Pascals"*"Seconds"];
L = Quantity[200*10^-9, "Meters"];

D = (KB*T)/(3*Pi*eta0*L)

This evaluates to:

$2.41258\times10^{-12}\,\text{kg}\, \text{m}\text{/(}\text{s}^3\text{Pa})$

Which under UnitSimplify reduces to:

$2.41258\times10^{-12}\,\text{V}/\text{T}\,\, ... \,\,(volts\,per\,tesla??)$

for diffusion coefficients I am expecting units of $meters^{2}/second$.

Can anyone see whats gone wrong?


share|improve this question
up vote 4 down vote accepted

UnitSimplify simplifies the units it doesn't guarantee it'll give you the units in SI. Just use UnitConvert, it gives you the answer in SI units.

UnitConvert[(KB T)/(3 Pi eta0 L)]

Mathematica graphics

share|improve this answer
Oh thanks. So what exactly is happening when it gives me V/T? – Steve Hatcher Mar 31 '14 at 6:03
@SteveHatcher Well, 1 Volt is equivalent to 1 kg m^2/(s^3 A) and 1 Tesla is equivalent to 1 kg/(s^2 A) so it is actually correct that 1 m^2/s is equal to 1 V/T – RunnyKine Mar 31 '14 at 6:17
oh great. thanks – Steve Hatcher Mar 31 '14 at 6:26

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