Why is the simple linear pressure equation insufficient for precise pressure calculations across large vertical distances in gases?

Answer

Gases are highly compressible, causing their density ($ ho$) to increase significantly with depth/pressure

Because gases are compressible, density ($ ho$) changes significantly as pressure increases with depth, meaning $ ho$ is not constant, requiring more advanced calculus and integration for precise calculations.

Why is the simple linear pressure equation insufficient for precise pressure calculations across large vertical distances in gases?

#Videos

How does liquid pressure change with depth- Kisembo Academy

depthpressurefluidhydrostatic