Confusion with Fluid pressure

Question

I have studied on the internet that gases exert equal pressure in all directions in a container but liquids do not. In liquids pressure exerted on the wall of a container increases with depth. Why is that so? any logical or intuitive if not conceptual answer is also appreciated. Also can there be a situation in which liquid can exert equal pressure on the walls of their container, independent of depth?

Note: I found a pretty similar question here but is a bit complicated and so I couldn't understand it. Also please use liquid/gas terms instead of fluid as it mixes up things for me.

Answer 1

I have studied on the internet that gases exert equal pressure in all directions in a container but liquids do not. [...] Why is that so?

Actually they both work in the same manner. The cause is the presence of gravity.

Pressure increases with depth in a liquid, because the heavy (dense) liquid has to carry the whole column of liquid above it. A water particle at the bottom of the sea must hold up all the water above it and all the air above that. The water particle at the surface only has to hold up the air above it (corresponds to standard atmospheric pressure).

It is the same thing for air and other gases. And as you might already know, the atmospheric pressure at ground level is much bigger than the atmospheric pressure at an air plane in a height of 10 km. Just watch any aircraft crash movie and see how everything is suched out when there is a breach because of the lower outside pressure...

For gas within an earth sized container, the pressure difference because of depth is so small because of the very low density that it simply doesn't have to be considered.

Also can there be a situation in which liquid can exert equal pressure on the walls of their container, independent of depth?

Yes, in outer space where no force like gravity pulls all particles in one single direction so they have to "carry" reach other. But in that case it would also be difficult to define depth...

I should mention though that such liquid in outer space of course exerts it's own gravitational pull. If you have large quantities of liquid (or gas for that matter - just look at a gas planet), and I mean very large quantities, then the liquid will form a sphere and the pressure will increase as you dive deeper. But this depth is then measured towards the center of this sphere.

Answer 2

I'll expand a bit on my comments to the question here.

For fluids, the pressure is generally written as

$P = \rho g h$

where $\rho$ is the density of the fluid, $g$ is the gravitational acceleration constant, and $h$ is the depth. The pressure increases with increasing depth because the weight of all of the fluid on top is pushing down, and the further down you go, the more fluid is above.

Now, we must consider that gases themselves are also fluids, so the same thing must hold true for gases. However, in the case of a gas, the value of the density is very low, so for any reasonable size storage container for a gas, the pressure due to gravity will be very small. However, for large quantities of a gas, the Earth's atmosphere for instance, this now comes into play, since the height of the atmosphere is so high. We feel this difference as barometric pressure, and at higher altitudes (lower depths), we don't feel as much pressure due to exactly this effect.

The pressure of gases can also be affected by the temperature of a gas unlike a liquid. In a liquid, the loose interactions between the particles hold them together that don't allow the particles to move freely away from each other like in a gas. But in a gas, the particles can move freely. For an ideal gas, you have a relationship for the pressure that looks like the following:

$P = \frac{Nk_BT}{V}$

where $N$ is the number of particles, $k_B$ is a constant, $T$ is the temperature and $V$ is the volume of the container. In this case, you have a constant pressure on all the walls of a container. This is the dominant effect for gases that are stored in any reasonably sized container, and this is where the difference between gases and liquids arise.

For having a liquid exert equal pressures on all container walls, you would have to remove the effects of gravity.