# Confusion with Fluid pressure

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.

• Can you link the similar question that you read? – Bernhard Oct 17 '15 at 11:33
• @bernhard it might not be the same but is related. physics.stackexchange.com/q/110237 – Freelancer Oct 17 '15 at 11:46
• It might have something to do with scale. Certainly, air pressure due to the atmosphere changes with altitude, and is at a higher pressure at lower altitudes – tmwilson26 Oct 17 '15 at 11:47
• @tmwilson air pressure ?? Where did that come from !!! I don't think I even mentioned it in my question !! Please explain what you are trying to say. – Freelancer Oct 17 '15 at 11:49
• You say that gases exert equal pressure in all directions in a container. Air in the atmosphere is a gas. If you put a large container (impossibly large I admit) around it, it would not exert equal pressure on all the walls of the container. The reason liquids exert higher pressures at larger depths is because of gravity. On any reasonable scale for a gas, I assume that gravity is ignored when considering pressure differences. (To add to this, fluid pressure is $\rho g h$, where $\rho$ is the density of the fluid, and gases are very dilute fluids) – tmwilson26 Oct 17 '15 at 11:53

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.

• Ok!! I understood with increase in depth pressure at the bottom increases with height due to effects Gravity. But I am not able to understand why the pressure exerted on the side walls also increases with height the bottom surface is fine but why with increase in depth the particles exert more pressure at the side walls .. I have the same problem with steevens answer also .. Please read the comments I left above... – Freelancer Oct 17 '15 at 12:58
• This is because of the buoyancy force which exerts pressure in all directions an object. In this case, the object can be considered to be more of the fluid or the container walls. The wikipedia article on Buoyancy will do a better job explaining this effect than I can do in this limited space. --In particular, see the section on 'Forces and Equilibrium' – tmwilson26 Oct 17 '15 at 13:19
• I studied it and drew some conclusions are they right ???......can I say that the air pushes me with equal pressure on all sides!!?? So by this analogy the molecule of water near the side push the side wall with pressure equal to that they are experiencing from the up!! And as with height The pressure from up or gravity increases so that the pressure exerted on the side also increase by the logic I gave here ...right.. – Freelancer Oct 17 '15 at 13:45
• Essentially yes, think about the following: If you squeeze a fluid from the the top and the bottom, it will tend to want to push out the sides (if you have no side walls for instance). With side walls present, you can push the fluid from the top and bottom, the fluid will try to move out the sides but can't because of the pressure exerted back on the fluid by the side walls. – tmwilson26 Oct 17 '15 at 14:11
• Can you clarify this also... – Freelancer Oct 17 '15 at 14:19

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.

• I understood the sea example you talked about and how pressure exerted on the particle at the "bottom" of the sea is more than the pressure experienced by a particle at the top ...and that explains why pressure on the "bottom" surface increases with depth!! OK done!!but... – Freelancer Oct 17 '15 at 12:36
• But .......I am not able to see how we can say the same thing for the particles on the side why the particles at the top exert less pressure on the side whereas particles on the bottom apply more pressure on the side of the container ??? – Freelancer Oct 17 '15 at 12:40
• I read an experiment in which a hole was done at the side near to ground and then at the top on the side in which the water through hole on the lower side came faster as compared to the one at the top ....si that means i am right...and you gave a nice explanation of the height thing can you extend it a bit more to the particles on the side.. – Freelancer Oct 17 '15 at 12:41