# Transfer of of force and pressure in a liquid.

I have the following question/problem of understanding:

I am thinking that the only way force or pressure can transfer in a liquid is by water molecules pushing other water molecules, pushing other water molecules etc. If I put a certain pressure in a closed tank to a certain number of water molecules, and let's say the container get's wider the further away you go from where I apply the pressure, why doesn't the force get divided by the water molecules that are in contact with the ones that I am pushing on?

In other words, if I apply a 1 kg/cm2 pressure to however small area of a closed tank, every 1 cm2 of the tank gets the same pressure. How does the force transfer? If I put a pool ball on top of two pool balls, the force gets distributed between the two bottom pool balls, but how does it work in a liquid such that every water molecule gets the same force?

## Answers and Replies

sophiecentaur
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That's a fair enough model to start off with. You need to add the fact that you have random thermal vibrations throughout any material to explain how forces tend to be transmitted through the bulk by more frequent collisions from a high pressure region against a low pressure region.

But why doesn't the force get divided by the area?

I can understand that if the tank doesn't get wider, then if I look at a 2-dimensional cross section, one water molecule pushes two molecules under it, but the one next to it also pushes the one below it etc, so the force would remain the same if the tank doesn't change shape, but how does the force transfer to every cm2 of the tank if it gets wider at some part? If there are more water molecules to push by the same number of molecules, why doesn't the force get divided by the area?

This is actually a good question.

You must remember that liquid molecules are "free", so if you have any net force on a volume of fluid, it WILL move; it will move until something else (such as the walls) push against it with enough force to cause zero net force on it. At this point, the fluid is in equilibrium.

The fact that pressure is the same in all directions is interesting, but nobody can really convince you of it, you have to think about it on your own and you'll understand it after a while. Just keep imagining situations where you have less pressure on one part of the fluid, and imagine how the fluid will adjust itself until the pressure is equalized.

sophiecentaur
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Yes - if there is a local difference in pressure, a fluid will flow until the pressure is equal - it has no strength to withstand a pressure difference without moving. An ideal solid, otoh, will not flow and will not 'transfer' any force sideways.

@chingel Your argument, based on forces misses out the fact that any given molecule will move in whichever direction encounters least reaction force. If there happens to be no 'sideways' force, a molecule is just as likely to flow sideways as in the direction of the original force that pushed it. Once you accept that a molecule can move sideways then it can produce a force (pressure) on the side of the container (or even up, underneath an overhanging surface). You are actually not too wrong in your argument if you just apply it to what happens at the time the force is applied initially. Most of the statements about molecules and pressure describe the situation when things have settled down (this could be within less than a microsecond, in some media but longer for a low pressure gas).

This sort of misconception can also happen when discussing what happens to the current in electrical circuits (i.e you have to wait till things settle down to do simple calculations).

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I can understand how the force gets transferred sideways, they aren't exactly on top of each other, they have random motion, any force at a slight angle will make them move in the direction of least resistance etc.

But why doesn't the force I apply to a small section of a tank get divided by the whole area of the tank, but instead the same force gets applied to every section of the same size?

If I have a triangular container, one molecule deep, one molecule wide at the top and 10 molecules wide at the bottom, getting one molecule wider per row of molecules. If I apply a 1 N force to the top molecule, wouldn't the force it applies to the two molecules below it be divided by them, so that each gets 0,5 N of the force? And at the end, wouldn't the pressure be 0,1 N per molecule?

sophiecentaur
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The initial force you apply does get 'shared out' and there will be a finite movement. Movement will stop when the forces all balance. This takes time, as I said. Once the forces of reaction from the walls have balanced then the process that you are worrying about are over.

But why doesn't the force I apply to a small section of a tank get divided by the whole area of the tank, but instead the same force gets applied to every section of the same size?

The force does get divided by the whole area of the tank and results in a lower stress than the stress in your applicator. Force doesn't change, area does.

Stress = Force / Area

But why doesn't the force get divided by the area?
It does get divided by the area. You are confusing force with pressure. Pressure is defined as force per unit area. At an air pressure of 1000 hPa, a ten square meter surface will experience ten times as much force as a one square meter surface but experience exactly the same pressure.