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# sonic needle valve question

```hi all,
i don't know if anyone replied to this issue or if anyone cares but i saw
this posting and,having no actual interest in the practical issues of the
thread,
thought it made a good thought exercise. The question is is it reasonable to
think co2 could be moving through a needle valve at the speed of sound?
here goes:
depending on air temperature and humidity sound moves at about 345 meters/s
under standard conditions.  that's 345,000 millimeters/s. now, i have no idea
what the dimensions of a needle valve are, so for the sake of the exercise i'll
start by assuming a cylindrical chamer 1mm in diameter and 1 mm in length. for
the moment we can disregard pressure and density and use conservation of mass
to say that whatever enters the valve chamber must come out of chamber.  the
volume of the chamber is the area of the circular cross section multiplied by
the length, or pi X .5mm squared times 1mm = about .785 cubic mm. now, the speed
of sound is 345,000 mm per second, or 1/345,000 = 2.9 X10^-6 seconds to travel
a mm.  that means that if the co2 in the chamber is traveling at the speed of
sound
it will take 2.9 microseconds for the co2 entering the chamber to leave the
chamber. so .785 cubic mm is expelled every 2.9 microseconds.  another way to
say this is that since the chamber is 1mm in length the co2 will travel the
length of the chamber 345,000 times per second. times a volume of .785 mm cubed
= a volume of over 270,000 cubic mm coming out of the valve. that's a cube of
co2 about 6.5 cm on a side.  that's a big bubble. now, if your using a lot of
co2
and the valve chamber is much smaller its possible that this is reasonable.
of course, this assumes that the co2 entering the valve chamber is at
atmospheric
pressure, which is probably not true. well, that was fun, eh
cheers
elie

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