How do you figure out the air pressure in a deep mine shaft or cavern? Does the shape and direction of the shaft matter or is it purely a function of depth?
Any difference not due to depth alone would quickly be equalized by the movement of air-- assuming that the mine is open to the surface.
Caves and large mines tend to “breath”. It takes a little pressure to move this air against the restriction of the passage(s) to the surface, so the topology does make a slight difference.
In the rare moments where the flow is reversing, pressure is a function of depth, barometric pressure, and averaged air temperature within the cave. It is a fallacy to think that a funnel shaped vessle concentrates pressure toward the point.
Breathing and temperature fluctuations aside, this Pressure Altitude Calculator probably isn’t too horribly off.
It gives 2 atmospheres pressure (or 1520 mm Hg) at an elevation of 20,495 feet (3.88 miles) below sea level.