When and why Does Pascal's Law Work?

why is it that pressure applied at a point in an enclosed fluid has to be transmitted equally throughout the fluid? bearing in mind that different points of the fluid are going to be at different heights from the force being applied
- bradley juma (age 16)
Nairobi,Kenya

That's a great question, which we've answered before, in the first follow-up here: https://van.physics.illinois.edu/qa/listing.php?id=2231. The key point is that this equal-pressure-change-at-all-heights rule ("Pascal's Law") only works when the changes in density ρ are very small compared to the pressure change divided by gh, the gravitational field times the height difference between the regions. That tends to be true for nearly incompressible fluids or for gases with small densities, so long as very large height changes aren't considered. 

As an illustration that the rule can't be universal, think of what would happen if some extra gas were released raising the air pressure slightly near the Earth's surface. That wouldn't have any noticeable effect on the pressure  at heights of say 10000 km, since there's almost no atmosphere there.

Mike W.

(published on 11/20/2014)