Here's how I did it. My trusty chart of the 1958 ICAO Standard Atmosphere
says that about 10^-10 of the mass of the atmosphere is above 150 km. I
assumed that all the air above that height was expanding freely horizontally
into vacuum, which would give it a velocity equal to the speed of sound, or
282 m/s at that altitude. Thus, 10^-10 of the atmosphere disappears in a
time equal to the time required for sound to cross the width of the ring.
The rest is multiplication. (hmmm... missed a factor of two there; should
be half the width of the ring, because it's spilling off both sides.)
Obviously the dynamics of the gas is a little more complex than this. But I
don't think I'm off by more than a small factor.
Zoom,
--CarlF