if a problem is solved this way: there is a cave with the entrance submerged in

Question

if a problem is solved this way:

there is a cave with the entrance submerged in a lake. we want to find the air pressure inside the cave. we used P=P_0 + rho*g*depth or P_0 - rho*g*height for the water pressure, we assumed the air pressure to be fixed inside the cave. Why did we make such as distinction?

A) the pressure relation is valid for water, not air.

B) the pressure relation assumes the material is incompressible. Air is compressible.

C) the equation is valid in the cave.

D) the equation is valid for the air in the cave with the height being the height above the water level. However, P_0 equals the water pressure at the surface, and rho (the air density) is far lower than water density. It's valid to ignore the rho*g*height term.

E) there was some other reason we ignored any height term inside the air in the cave.

Explanation / Answer

D) the equation is valid for the air in the cave with the height being the height above the water level. However, P_0 equals the water pressure at the surface, and rho (the air density) is far lower than water density. It's valid to ignore the rho*g*height term.

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