I am confused. Since the thermal motion speed of air molecules is about 500 meters per second, why is the air speed of a general fan less than 500 meters per second?
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$\begingroup$ To piggy back off gandalf61’s nice answer: the Maxwell Boltzmann distribution is orientation agnostic. It only gives you the probability of a certain speed for a molecule. Thus, if you think about “still” air, on average the particles are moving with zero velocity even though each one is moving quite quickly. But an object like a fan makes the average speed of some subset of molecules have a net orientation in a particular direction, which we feel as a rush of air. $\endgroup$– Matt HansonCommented Oct 27 at 13:29
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$\begingroup$ @MattHanson That is to say, the air molecules have a net velocity in the direction of the air's velocity? The fan blades make the air molecules have a net velocity in the direction of the air's velocity? $\endgroup$– enbinCommented Oct 27 at 14:14
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1$\begingroup$ You can think of it as a shift in the average directional velocity of the particles, yes. Basically, the speed of the air molecules isn’t particularly different, but just redirected to have a useful net effect rather than just exerting pressure on the surfaces of objects in their vicinity. $\endgroup$– Matt HansonCommented Oct 27 at 14:22
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Because thermal motion of individual air molecules is a random walk, whereas the speed of the air stream created by the fan is a co-ordinated movement of many molecules averaged over time.
Imagine millions of impatient and indestructible bumper cars bouncing off one another in a very slow moving traffic jam.
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$\begingroup$ That is to say, the air molecules have a net velocity in the direction of the air's velocity? The fan blades make the air molecules have a net velocity in the direction of the air's velocity? $\endgroup$– enbinCommented Oct 27 at 14:14