*Originally posted by @twhitehead*

**http://www.cleverly.me/diy-ac/?ref=fb
**

https://www.youtube.com/watch?v=oSbZWNk84F4

https://www.youtube.com/watch?v=Oh9LhrLGUc4

I came across this claim that blowing air through a cut bottle somehow cools it down. I don't believe it should work and the explanation given is rather weak.

Does anyone have any ideas as to whether this should work, and if so, based on what principle?

I feel like it violates the Second Law of Thermodynamics, but its hard to tell without some serious thought. Also, I'm no expert in the fields of Fluid Mechanics/Thermodynamics.

Working "outside" the second law (complete idealization) I can see one way it works, using three principles.

1) The Ideal gas law

2) Bernoulli Prinicple

3) Continuity

Number "3" first: Continuity

The volumetric flow rate entering the bottle is equal to the volumetric flow rate exiting the cap. This means the flow is incompressible ( this is not exactly true, but probably close enough for this case...the pressures are not changing much). Hence the average velocity exiting the cap is greater than what is entering.

Number "2", Bernoulli principle is applicable to idealized invicid flows.

It states the pressure head + the kinetic head+ elevation head is constant along a streamline in a flow field. It means energy is conserved or the gain in kinetic head at the cap was provided by a drop in pressure at the cap. The elevation remained unchanged.

For your reference in Fluid Mechanics Head is a specific Energy (Energy per unit mass). Calculations are typically done with this metric.

Finally, #1 the Ideal gas law for adiabatic process ( without heat transfer) states the Pressure to Temperature ratio remains constant for an Ideal gas such that the temperature at the cap is equal to the ratio of the pressures times the temperature of the entering air.

T_cap = P_cap/P_entr.*T_entr.

P_cap/P_ent < 1

T_cap < T_entr.

So under completely idealized conditions the models I used do not explicitly forbid it.

**However**, the second law states that in any real process entropy is generated.

Conservation of energy and the second law invalidate Bernouliis principle for "real" viscous flows with a head loss term ( that is heat is generated from friction through the exchange)

The Energy Equation for this case states: pressure head + kinetic head + elevation head at the entrance is equal to the pressure head + kinetic head + elevation head + head loss

The head loss term is really a group of terms that represent the thermal energy of the flow ( sum of internal and transfered heat) across the boundries. By the second law it is always positive. This means that the change in internal energy of the flow is always greater than the heat that could could be transfered out between the two reference points. As a consequence, the internal temperature of any "real" flow necessarily increases in the direction of the flow.

So I'm going to say it violates the second law, and is actually not a real phenomenon.