Why Is Fan Suction/Intake So Weak Compared to Exhaust?

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I’ve Googled this and the general responses I’ve seen are that a fan’s intake is designed such that it “sucks in” air from all around it (left, right, up, down … with a very wide area that it draws from), but it exhausts/shoots out air in a “jet stream.”

But why is that? I’ve looked at a fan’s blades and frame and it still doesn’t make sense. Like my house fan’s exhaust/exit part is the same size as the intake. It’s not like the exit is “focused” through a narrow tube to concentrate the path or strength of the air. But, clearly, every fan does have stronger exhaust. If you stand it front of it, you can feel strong wind, but if you stand behind the fan, you literally notice nothing. You need to place a piece of lightweight tissue paper near the back of fan to even notice any air suction.

If it’s not the exhaust frame (like a narrow opening/tube) that creates a much stronger force, what is it that does this?
 
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The fan lowers the pressure at the inlet. Air from all directions begins to flow toward the fan, turning gradually as it accelerates, onto the axis of the fan.

Once accelerated by the fan, the air has momentum that carries it away from the fan outlet, without any need to immediately spread out again.
 
It feels like there must be a deeper reason for this.

In principle, the laws of physics are symmetric and time reversible. If the input to a fan is omnidirectional, there is no reason in naive principle why the output of a fan could not also be omnidirectional.

But in fact the output is directional. So it would seem that entropy has to figure in somehow.

A fair bit of skull sweat has gone into analyzing the conundrum. https://en.wikipedia.org/wiki/Feynman_sprinkler
 
Had my central air system checked when it sortta wasn't working. I guess I hadn't replaced the filter. Guy suggested I might want to get a UV filter accessory. He said it would "kill bugs and particulates". I know UV can kill the former, not sure how he thinks it's gonna murder the latter. Now I'm finding out there's more than one type of UV filter: one for the air flow and one for the coil. He was suggesting we might get one for the air flow, but now we'll have to change the bulb...

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