# Reason for fluid pressure

What is the physical reason that high pressure regions (say, of air or water), want to expand into low pressure regions? What force is causing them to "equilibrate" the pressure?

The only thing I can think of is that in liquids (or gasses) all molecules are repelling each other, meaning that in the absence of other forces (like gravity) they would disperse as far apart from each other as possible. But it doesn't seem like that could be true of all gasses and liquids (that the molecules repel each other). For example, water is polar and I'd think the positive/negative sides of the molecules would attract. Not to mention Van der Walls force. Is there some repulsive force that overcomes all other attractive forces, or is there something else entirely that I'm missing?

I'm interested in a mechanical/physical reason that this should happen.

• You forgot kinetic energy of molecules and collisions. Jul 1, 2016 at 5:23
• Ok, that begs another questions which I shall post separately! But I think you're saying that the "random" motion of particles due to temperature forces them apart from each other, and this force overcomes any attractive forces. Aug 9, 2016 at 17:25
• That's the point but that's not all, other factors too would be involved that I can't guess for now, like conservation of momentum etc. Aug 10, 2016 at 8:01

Interactions between the molecules of the gas are not required. In fact ideal gases are modeled as if the molecules have zero interaction.

They do however move and interact with the container. That is sufficient to explain the behavior.

Imagine that you have a vessel with two identical halves that are connected by a small portal that can be opened and closed. Put in gas so that one half is pressurized more. Assuming each half has the same volume, and the gas is all at the same temperature, then the only way for it to have more pressure is to have more molecules inside.

Now, open the portal. Even though none of the molecules of this ideal gas push each other, there will be more that reach the portal from the higher pressure side than do from the lower pressure side. Over time, this leads to a bulk flow in the same direction.

In thinking about this more, this explanation says that the mere fact that there are more molecules in one container causes bulk flow into the "low pressure" continainer. But: why is there flow at all?

The idea isn't "there are more molecules" and you're done. The idea is:

• There are more molecules (but all the molecules are the same)
• they have the same temperature (which means the average speed is the same)
• leading to the idea that there are more collisions per area on the high-pressure side

If one side has a thousand molecules and one has a million molecules, the one with more will have a greater chance of striking a specific-sized target over a period of time.

Now instead of a random target, let's pick the valve barrier (still closed at the moment). We count the molecular collisions against that barrier for one second. We'll find that the high-pressure side has more collisions than the low pressure side.

So what happens if we remove the barrier (open the valve)? It means that on average, more molecules will reach the barrier from the high pressure side than reach it from the low pressure side in the same period of time. With no barrier in place, most of these molecules will go through the valve to reach the other side. That difference in rate of molecules reaching the valve is what leads to the bulk flow.

• Thanks! I wondered this as I was looking out the window of an airplane - the "container" there would be the surface of the earth, and the force of gravity somehow? Jul 1, 2016 at 14:44
• In thinking about this more, this explanation says that the mere fact that there are more molecules in one container causes bulk flow into the "low pressure" continainer. But: why is there flow at all? Why don't the particlees sit happily in the container they were in? I'm not seeing how the container causes motion. It seems like this answer presupposes that the particles want to equilibrate - what am I missing here about how the containers cause this equilibration force? Aug 9, 2016 at 17:21
• @Demis, Because the molecules hit randomly, sometimes they hit the hole between the containers. They don't "want" to switch at all. But some fraction will find the hole. But the more molecules bouncing around hitting things on one side, the more that will strike that hole. Aug 9, 2016 at 17:33
• Thanks, so the physical reason does originate from the interaction between molecules (kinetic-energy/collisions), although the container is all that's needed once that interaction is assumed. Aug 9, 2016 at 17:52
• @Demis, imagine instead the molecules bounce off the walls only (that they are so small they always miss each other). This is the ideal gas limit. Aug 9, 2016 at 18:30

According to the second law of thermodynamics,entropy of an isolated system tends to increase. Considering the high pressure region and low pressure region as an isolated system, its total entropy goes up, making fluid flow from high pressure to low pressure to increase the disorder(entropy of the system).This behavior follows from statistical models of fluids and their random motions.

• Sorry I don't have a good intuition for Entropy at all, or what that physically arises from. You're saying that the heat of each molecule, which produces said Random Motions, is the force that makes each molecule bounce against each other, in effect repelling each other (and overcoming all repelling forces)? Jul 1, 2016 at 14:46
• Thanks for the answer! Why is an area with higher density considered "more ordered", in an amorphous system such as fluids? And what's the PHYSICAL reason that order much go down vs. time? I'm looking for a mechanical explanation behind the laws & equations. Aug 9, 2016 at 17:23