Comment by generuso
21 hours ago
Cold gas thrusters used in space applications typically produce 60-70 kgf of thrust for 1 kg/s of gas flow, which means the average axial velocity of the jet is just under 600-700 m/s. It is a little more when the gas expands into vacuum and a little less when it expands into ambient air at the sea level.
How fast the gas expands through an opening depends on the pressure ratio between entrance and exit, and for ordinary air the flow reaches the speed of sound at the narrowest part when the pressure ratio exceeds about a factor of two. The flow never becomes supersonic in the constriction itself, but after the constriction the flow can continue to accelerate to supersonic speeds, especially if the constriction is followed by an expanding nozzle (converging-diverging, or de Laval nozzle), although this is not strictly necessary. For example, one can observe shock diamonds in the air coming out of an ordinary plastic bottle filled with slightly compressed gas: https://www.youtube.com/watch?v=61tsXGUc6nU
Thanks for the clear explanation, and you deserve a separate upvote just for that video link. "slightly" -- compared to what Tesla is claiming, sure, but 5+ bar is no joke -- "you'll put an eye out, kid"
I wonder if the shock waves visible in the video are still due to the converging-diverging aspect, just with no bell around the diverging part.
If we look at the flow lines, they converge and diverge even when the "nozzle" is a section of a pipe.
In rockets, there is a so called "aerospike" engine [1], which does not have any bell-shaped nozzle at all, but instead uses the ambient air to always shape the flow for an ideal expansion ratio. In theory it is great, but in practice it remained mostly a pie in the sky.
[1] https://en.wikipedia.org/wiki/Aerospike_engine