If I have a closed container of a given height $(h)$, located at a given distance from the centre of the Earth $(r_o)$, what would the pressure difference be at the top of the container vs the bottom?
I was looking at this video, and it was explaining that the pressure of a fluid is $P = \rho h g$, where $\rho$ is the density of the fluid, $h$ is the height of the liquid on top and $g$ is the gravitational force.
However, I think that refers to an open container and also as my height may be as little as $1$ m and as big as $10^7$ m, I'm not entirely certain that I can use this formula as $g$ can very significantly, which would appear to invalidate the mass calculation that was used to arrive at that formula $F = m g \rightarrow F = (\rho V) g \rightarrow F = (\rho A h) g$ , since density can very over height. Also, $\rho$ would depend on temperature, pressure and volume, so that makes this even more complex, so I don't even know where to start.
