The Impossibility of Flying Heavy Aircraft Without Training

But in the closed system
that consists of the airplane and the atmosphere, or the fan and
the air in the room, momentum is conserved, just as mass and
energy are.

Except that that's not a closed system. You need the earth to close the
system. No earth but phantom gravity, and to conserve momentum, the air
will continue to downflow, which is what would happen.

If only some of it does, then mass is not conserved. ALL of it,
or rather an equivalent amount of displaced mass makes it
back to the inlet of the fan.

No, mass can be conserved by having some of it pile up. This is in fact
what happens. The pressure on one side of the room goes up. Guess why.

In te case of the aircraft, the fan is moving through the air so that
when the air (or rather an equivalent displaced mass of air) returns
to the inlet, the inlet has move on.

In the case of the aircraft (propeller), the air does not return to the
inlet. It keeps on being blown back, since there is no wall to stop it.
The momentum stays with the air and the earth (which starts to spin a
little one way) until the airplane lands, and pushes the earth the other
way. Momentum is always conserved.

Jose
--
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