Air in a tunnel
A classmate of mine and I got into an "elevated voice" discussion over the following idea:
Let's say that we were able to drill a hole through the center of the Earth and out the other side. The atmosphere is allowed to flow freely through this tunnel. Making all the prettifying assumptions (such as the Earth is homogenous, the temperature at the core doesn't affect the air in the tunnel, the tunnel is of sufficiently small size to not significantly affect the value of sea level pressure, etc.), would the air pressure in the center of this tunnel be higher, lower, or the same as sea level pressure?
My friend believes that it would be a significantly larger maximum at the center, as the air column would compress the air all the way down there.
I assert that the air would follow the gravitational potential, having a maximum at the surface and a near-zero pressure minimum at the center.
Any insight?
Let's say that we were able to drill a hole through the center of the Earth and out the other side. The atmosphere is allowed to flow freely through this tunnel. Making all the prettifying assumptions (such as the Earth is homogenous, the temperature at the core doesn't affect the air in the tunnel, the tunnel is of sufficiently small size to not significantly affect the value of sea level pressure, etc.), would the air pressure in the center of this tunnel be higher, lower, or the same as sea level pressure?
My friend believes that it would be a significantly larger maximum at the center, as the air column would compress the air all the way down there.
I assert that the air would follow the gravitational potential, having a maximum at the surface and a near-zero pressure minimum at the center.
Any insight?