fluid dynamicsnewtonian-mechanics
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.
The reason is that you have a boundary layer on the surface of the blade of the fan. On the frame of the blade (the blade moves with some velocity, but at the frame of the blade the air moves) the boundary layer starts from the surface of the blade where the fluids velocity is zero and as you move away from the blade, the velocity increases up to the value of the velocity of the blade (you can call that the undisturbed velocity of the flow).
So if you have some fine dust, it actually doesn't feel much wind and it can't be blown away. Static electricity could be an other factor, but you can see that on metallic propellers also.
It is called Venturi Effect.
The increase in speed of the air surrounding your vehicle comes with a decrease in pressure. That explains too why a chimney works better in windy days.
The Venturi effect is explained by applying the Bernoulli Equation (say, the conservation of energy of a small piece of fluid that moves within the flow) between two points along a streamline (in this case, we would follow a piece of air in a tunnel wind)
$\frac{1}{2} \rho v^2 + \rho g h + p = \text{constant}$
The increase in the first summand when the flow gains speed to adapt itself to the shape of the car, is compensated by a decrease in the pressure $p$. Look what happens in this picture (wikipedia) when the flow changes speed to adapt to the shape of the tube:
(Image from wikipedia) $ $
Note the similarity with the high school equation for the conservation of mechanical energy of a particle:
$\frac{1}{2} m v^2 + m g h = \text{constant}$
(Just change the mass of the particle for the mass of a fluid volume unit, i.e. density, and add an additional summand to accout for the pressure, and you have Bernouilli's equation)
Bernouilli's equation is meant for an incompressible flow (water) which here means that the numerical results would be approximate, but qualitatively the same effect happens.
A related, interesting fact, is that submarine propellers must be carefully designed, in order to avoid points in which water suffers much too rapid a speed increase. When that happens, pressure becomes so low in that points that vacuum bubbles appear. The power released by the implosion of that bubbles against the surface of the propeller, not only is noisy, but also may damage the propeller itself. The phenomenon is called cavitation.
(Image from wikipedia)
Best Answer
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.