# Darcy law yields extreme speed for gas flow throgh packed spheres?

The darcy law is as follows: $u=-\frac{k}{\mu}\nabla p$.

Assume we have a gas, then $\mu$ is about $10^{-5}$. $k$ for packed spheres a few mm in diameter is of order $10^{-8}$ $m^2$. Say the pressure difference across a 0.1 m bed is 10 Pa.

Then we get $u= 0.1$ m/s which seems really high for such a small pressure difference. I mean, tens of Pascals is a variation which is comaparable to random pressure fluctations. Is this reasonable?

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It's difficult to assess how reasonable your figures are unless you specify units for all of them. This will also help to check that you've done the right calculation. –  Nathaniel Jun 20 '12 at 20:18
Everything in SI. –  tiam Jun 27 '12 at 13:37
What makes you say that the speed is unreasonably high? –  kleingordon Jun 27 '12 at 18:10
Because I gave a hard time imagining 10 Pa pressure fluctuations cause a 10 cm/s speed in a packed bed. I am modelling combustion in porous media and it is very sensitive to velocity: $u=0.05$ m/s and $u=0.25$ m/s can yeild quite different results. And accoring to Darcy's law it seems that velocities would fluctate randomly in those value ranges because it is a matter of a few Pa fluctuations in pressure. –  tiam Jun 28 '12 at 13:05