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Does the rotation of ceiling fan makes air circulate in a spiral, circular motion beneath the radius of fan or the air from outside is also mixed with it and replaces the air in room?

A specific example would be room filled with smoke or else, does ceiling fan clears it by throwing the smoke + air mixture out or does it keep circulating the air. Given the windows are open and no wind is blowing outside in any direction.

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A ceiling fan pushes air downward, (or sucks it upward depending on the rotation direction), creating flow streamlines in the shape of a torus (the size of the room).

Basically then, the window is a cavity that has a flow moving past it. If the indoor air is moving vertically fast enough, there will be turbulent mixing between the inside/outside air. Just like when you open your car window while driving: the faster you drive, the more turbulent the mixing becomes, and the better the inside/outside air will exchange before being recirculated through the room.

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To know if air from the outside will be mixed in, you need to know if the static pressure in the room near the window is lower. If yes, air will blow in at that point. Of course this has to be compensated at another point (can be through the same window but at a different location by air going out (conservation of mass in a stable system).

So no general answer is possible. If the fan is 100m away from the window, it will probably have no effect. If it is very close, it will blow out smoke at the bottom and suck in air at the top of the window.

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Fans have a unique quality of balancing air. They can bring in air surrounding the fan and push-out the air existing there, where it is running, this will take time.Its a low pressure high pressure game.

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