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Imagine a small metal canister, with a narrow exit on the top. There is a sort of door covering this, with a metal plate that is removed from the side. The pressure inside of the canister acts as a propellant, launching the weapon forward and propelling it through flight.

My question is: would this work? Some reasons I can think of that may cause this to not work:

• Horrible accuracy


• The opening would have to be too small to be plausible


• The canister would run out of air instantly, and fall to the ground shortly after


• The cost/energy of producing them is ridiculous

Imagine modern or slightly above modern tech, and enemies at distances of +/- 50 meters.

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No, this is not practical

You mention in your question the concern that "The cost/energy of producing them is ridiculous", which implies you're concerned about this being a practical or mass produced weapon. From that perspective, no, this doesn't work, for the simple reason that you are firing your pressure vessel at the enemy, instead of using the pressure vessel to fire a projectile at them. The latter approach has historically been used extensively, and there is no justification for not taking this approach with pneumatic weapons.

• https://en.wikipedia.org/wiki/Ballistic_knife


• 
  https://en.wikipedia.org/wiki/Holman_Projector (originally powered by compressed air)


• https://en.wikipedia.org/wiki/Girandoni_air_rifle

In all of the video instances noted by @elemtilas, non-combatants are using extant pressure vessels in a very wasteful manner. With any of those devices, it would be more practical to use the large canister to fire larger number of lightweight projectiles, i.e. flechettes, and then still have the canister to use when you're done!

A resounding 'yes' at +/- 50 meters.

The compressed CO2 cylinders used in air guns have enough force to launch the cylinders at least 50 m.

They are used to propel rocket car models, rockets, and such. We had a stray (one that came out of the end of a rocket) ricochet back and forth in a classroom 20 m long. Left dents in several places in the walls. The trick would be to launch them in a tube just slightly larger than the gas cylinder. The firing pin would be exactly that - a pin that punctures a small hole in the nozzle end. We used a hammer and a nail. Put a hardened bullet-type nose on them, and maybe a trailing rigid tail or stability, and you would certainly have a weapon that would hurt.

These CO2 cylinders can be made quite inexpensively, although probably not cost competitive with bullets.

What you are talking about is really just rockets that use compressed air instead of a chemical reaction to develop pressure. Accuracy can be controlled using the same mechanisms such as tail fins. The duration of the propulsion with compressed air can be extended using reaction mass such as water, as mentioned in another response. Production costs will depend on many other factors that you control in your setting.

Compressed air is obviously inferior to chemical based propulsion since we (humans in general) know how to do both and we don't generally choose compressed air. I would venture a guess that the main problem is weight. Canisters that can handle high pressure gas are heavy. Adding reaction mass to extend the propulsion adds weight. If you add a payload such as explosives then you are adding more weight.

You should also consider whether your tanks contain compressed air (like a SCUBA tank) or contain gaseous mixtures in liquid form (like basically every other high pressure tank). The liquid will add even more weight but it also contains more potential energy than basic compressed air.