Jose wrote:
In open air the volume of air moving around the fan is larger,
but moving at a lower speed than the air moving through the
fan so that the momenta of the flow in either direction is equal
magnitude and opposite in direction to the flow in the other
direction.

Seems to me "almost equal" would make more sense, otherwise an airplane
propeller would not work. A propeller throws air backwards (alabeit
imperfectly); the airplane moves forwards in response.


For the stationary fan if it were only _almost equal_ then
you would eventually run out of air on one side of the fan.

Air molecules flowing through the propellor cetainly experience
momentum changes. But you can have a net flow of
energy without a net exchange of momentum because
momentum is a vector, energy is a scaler. If the airplane
is in level flight at constant speed it does not NEED to
gain any momentum from the propellor because the
momentum of the airplane is not changing. It needs
force to counter the force of drag.

Consider your example of the person who 'hovers' by
dribbling a basektball. His momentum is zero, the
momentum of the Earth is zero and the momentum
of the ball is constantly changing and reverses twice
each dribble. The dribbler is pumping energy into
the Earth yet there is no net exchange of momentum.

--

FF