It seems as though the vacuum of space should create a flow through the pipe since the pressure at each end is different. In fact, the air pressures inside the pipe will be the same as those outside the pipe, and all you will have done with your pipe is to wrap up a section of ordinary atmosphere. Because of gravity, the open atmosphere already has a difference in pressures between sea level and 50 miles above the ground.
Gravity pulls downward on the air and packs it together tightly near the ground.
Air's density and pressure near the ground are relatively large because this air must support the weight of all the air overhead. Air's density and pressure higher in the atmosphere are smaller because that air has less atmosphere overhead and supports less weight. With high pressure at the earth's surface and almost zero pressure 50 miles up, you might expect air to accelerate upward toward lower pressure. But it doesn't. That's because the pressure gradient, from high pressure down low to zero pressure up high, is just what's needed to keep the air in the atmosphere from accelerating vertically in either direction.