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In the following sentence, whose velocity is u—the particles or the medium?

For particles moving in a medium with macroscopic velocity u: The normalized Maxwell’s distribution function (Eq. 1.38) can be written as ..."

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    Prescriptive grammarians will tell you that the medium has the velocity, but in real life it's ambiguous; you have to use context to decide (which is why the author should have reworded it). Aug 18, 2014 at 10:54
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    It is a bit ambiguous, but since the particles are said to be moving and movement is often taking place in a medium that is considered static (or at least, the speed of movement is usually measured relative to the medium, as in a plane's air speed), I would assume the mentioned speed applies to the particles. That said, it could have been worded better.
    – oerkelens
    Aug 18, 2014 at 11:39
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    Ambiguity resolved easily by repositioning stacked prepositional phrases: for particles moving with macroscopic velocity u in a medium. If you don't mean to specify something about the medium, don't modify it with a prepositional phrase. Your readers will probably understand it, but why take the risk when doing it right is just as easy? Aug 18, 2014 at 14:02

2 Answers 2

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The key is the word macroscopic. In fluid dynamics the macroscopic velocity is a vector giving the magnitude and direction of the fluid. Individual particles within compressible fluids may have velocities that differ from the macroscopic velocity.

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The sentence is, on its face, ambiguous. However, it seems far more likely to me that the prepositional phrase, "with macroscopic velocity u," is modifying the participle "moving", and not the noun "medium". Presumably, it is the motion of the particles that is interesting in this situation. If it were the medium moving with velocity u, then we would seem to be lacking information about the motion of the particles within it.

Unless the context suggests that we're considering particles moving within a medium that is also moving, there seems to be little support for the idea that the medium has velocity u.

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  • Or perhaps the information about the motion of the particles is not lacking, but is rather what immediately follows after the colon.
    – RegDwigнt
    Aug 23, 2014 at 18:54
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    It appears that understanding the use of the phrase "macroscopic velocity" is also very helpful. I think Gary's Student got it right. Aug 23, 2014 at 18:56
  • @GTonyJacobs I think you are correct about the ambiguity. The sentence structure could be improved. Aug 23, 2014 at 19:19

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