TL;DR:
Destruction of the whole planet's ecosystem?
Ayup.
100km long, laid down east to west just above the surface of a flat land area
FYI, if the world you're building this on is like Earth, the ends of the tube will be about 200m above ground level due to the curvature of the planet's surface.
Or at least, it'll be this way to start with. I expect that the place where the tube just touches the surface will be subject to winds of terrifying speed and power that will generate massive dust storms that will rapidly excavate a deep trough, so most of the tube will end up being well above local ground level.
free fall for 100km until they exit at the west end
In a vacuum, the trip would take about 140 seconds, and you'd reach a terminal velocity of about 1.4km/s.
Because you're in an atmosphere, and the walls of the tube are entirely permeable, the actual speed of the wind through the tube is exceptionally difficult to calculate, as will be mass flow rates and pressures. So much so, I'm not even going to try.
And, to follow up, how much global effect would these winds have
As a parcel of air accelerates in the tube, the pressure behind it (towards the entrance of the tube) decreases, and the pressure ahead of it increases. This might not necessarily lead to catastrophically high pressures at the exit end and a vaccuum at the input end, because wherever the internal tube pressure is greater than ambient, air will move across the boundary of the tube.
Clearly though, the pressure at the exit will end up being higher than the pressure further upstream, and that pressure differential will generate winds.
Now, problem two: you've created a perpetual motion machine. Lets imagine you put a wheel at the boundary of the tube, with a portion of the rim inside the tube, and the wheel is mounted on a vertical axis.
The altered gravity inside the tube will pull the rim of the wheel, causing it to rotate. As each slice of the rim enters the tube, it experiences acceleration until it rotates out of the tube, at which point it escapes the magical gravity field and is only subject to air resistance. Until the object reaches its terminal velocity, it will be continuously accelerated by the alternating gravity field it is experiencing. Congratulations: you've invented a perpetual motion machine of the first kind.
Now, lets think about what happens next. Air will flow out of the exit end of the tube, creating a region of high pressure. Air will flow outside of the tube in the upstream direction into a lower pressure region, and diffuse back in to the tube.
This creates a toroidal vortex that is driven by a perpetual motion machine. It meteorology, this sort of situation is probably not considered a good thing.
I think that as the vortex grows and intersects the ground it will split into two contrarotating vertical vortices, like a pair of tornadoes. Its possible these will grow and eventually form a single giant vortex, but I can't say for sure. The whole thing is entirely too complicated to think about.
Quite how big and how powerful the resulting circular storm(s) will be I couldn't tell you. But I can say that they're being driven by a perpetual motion machine that can apparently provide an arbitrary amount of energy... there's probably some practical upper limit to air flow rates here due to weird compressibility factors, but you could develop supersonic wind speeds. Due to the speeds and volume of air involved, and the fixed position of the storm, it would strip up soil from the ground. The resulting dust clouds would be swirled round and sucked back into the tube and accelerated for free, so no energy is actually lost to the storm in lifting and accelerating material.
You'll eventually end up with continuous sand-hurricane at the exit... possibly a pair of contra-rotating ones. I'm not sure how big these could be. The centre of the storm might be 100km across to neatly fit around the source of its power. It will throw vast amounts of material into the sky, mostly dust. As it never tires, the dust might conceivably envelope the world, plunging it into gloom. If the tube was anywhere near an ocean, the ocean would probably generate huge quantities of water vapour which would in turn produce vast rainstorms and maybe even enough high-altitude water vapour to cause problematic greenhouse effects.
