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Accelerating a micron size particle in an air stream

Hi,

I have a 1m long, 10mm ID vertical tube attached to a vacuum system. I have a known flow rate of the air down the tube which is used to calculate the air velocity.

My question is if I then add micrometre sized particles (initially at rest) to the air stream what is their velocity at the end of the tube?

I know that eventually the particles will reach the same velocity as the air stream they are suspended in but is the tube long enough to achieve this?

I have spent a long time googling various ideas about this and have drawn a blank on a simple solution and it might not even be possible (simply), so I hand the question over to the collective wisdom of Physics Forums :)

Kind Regards

Craig

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