The gas tube of a carbine is 9.75 inches long if you straighten it out, so the gas has to travel about 10 inches to get from the gas port to the carrier cavity.
Looking at our graph in post #12 it takes a little less than 1/8 millisecond for the pressure appear at the cavity, so that means our gas has traveled a little less than a foot in a little less than 0.125 ms.
V(avg) = distance / time = a little less than (10/12ft) / a little less than (0.000125 sec) = a little less than 6,666 f/s
That's in the ballpark . . .
But, then there is the experimental data that shows:
https://i.imgur.com/5wPXAtj.png
. . . the peak velocity of the gas is around 1,500 m/s (4,921 fps, the red colored bit).
The speed in a carbine will be pretty much the same as the flow is choked to the speed of sound in the gas, despite the carbine having a slightly higher port pressure.
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