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How to calculate the energy required to disperse a certain volume of air?

Laboratory tests have shown, that air is 1.225kg/m³. Meaning over 5000kg of air is dispersed, how much energy is required? And would a timeframe be needed just like in cloud calculations?
 
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Depends on how it was dispersed and what the timeframe of dispersal was.

Normal one-directional dispersal? Normal KE: 0.5 * mass * velocity^2

Expanding omnidirectionally? (1/12) * mass * velocity^2
 
Depends on how it was dispersed and what the timeframe of dispersal was.

Normal one-directional dispersal? Normal KE: 0.5 * mass * velocity^2

Expanding omnidirectionally? (1/12) * mass * velocity^2
If it was a vertical cylindrical column of air?
 
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