Calculating the escape velocity of a pressurised gas

[sadben]

Well this question I've had since high school (first year mech), how would i calculate escape velocity of a gas if i know volume, diameter of the hole, pressure, temprature and mass.

 

[Simon Bridge]

Same as the escape velocity of anything... gas molecules are no different.

 

[sadben]

no i meant from a container like a gas canister or something something like this : http://www.sz-wholesaler.com/userimg/1068/1074sw1/co2-cylinder-for-lifejacket-799.jpg

 

[mfb]

If the diameter of the hole is small compared to the container (=> the gas in the container does not move in a significant way), you can look at a small volume of gas and use energy conservation: The pressure difference inside<->outside gives an energy density*, this energy gets released to accelerate the gas.

*to be more precise, I think you should use adiabatic expansion and calculate the released energy

 

[Simon Bridge]

At first I thought he meant gas escaping by rupturing the pressure vessel :)
My next thought was - adiabatic process... but it may be easier to treat it as isenthalpic for similar reasons: the gas is flowing at a steady rate and we assume no exchange of heat with the surroundings - and we are only interested in the speed right outside the nozzle.

Adiabatic would be more in the case where most of the gas is released in a burst wouldn't it?

The calculation still depends on the pressure difference, but also the specific enthalpy of the fluid. This speed can be further modified by the geometry of the nozzle.