The relation P = h rho g was derived for a fluid in a container, yet it is applied to open water and to the atmosphere. For which fluids does it hold only over depths where the density changes little?
AGases, because they are quite compressible
BLiquids, because they are quite compressible
CGases, because they are nearly incompressible
DLiquids, because they resist shearing forces
Answer & Solution
Correct answer: A. Gases, because they are quite compressible
1. The relation assumes a single average density throughout the depth considered.
2. Liquids are nearly incompressible, so their density barely changes with depth and the relation holds even to great depths.
3. Gases are quite compressible, so their density falls markedly with height and the relation can only be used where the density change is small.
4. Calling liquids compressible or gases incompressible reverses the two behaviours.
5. Resisting shearing forces is a property of solids, not of the liquids named here.
_Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.4 Variation of Pressure with Depth in a Fluid_
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