# Pressure in fluids

Fluids exert hydrostatic pressure because their molecules hit each other or the immersed body, but why is that at a greater depth pressure is higher when molecules are the same ?

Assume density of fluid is uniform throughout the liquid.

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Are you talking about the hydrostatic pressure? If that's so that is because under gravity you have basicaly more molecules at the bottom than above them. –  gatsu May 8 '13 at 8:24
Yes hydrostatic pressure . If you assume that the density is uniform everywhere , how can you have more molecules at bottom ? –  user23503 May 8 '13 at 8:26
In a liquid, the pressure is a very non linear function of density and therefore a slight change in density induces a big change in pressure. That is why in many problems of statics of fluid and or their dynamics, we can assume that the density is unchanged while it actually changes a little bit –  gatsu May 8 '13 at 8:28

## 2 Answers

Your statement:

Assume density of fluid is same throughout.

conflicts with your actual question

But why is that at a greater depth pressure is higher when molecules are the same?

If we imposed the very strict and non-physical constraint that the density of the fluid was uniform and isotropic, then we would have not variance in pressure what so ever - but as I have said this is non-physical.

What happens in reality is as follows... Each molecule in a given fluid has a mass. Gravity acts on this mass (lets assume vertically, and a column of perfectly stacked molecules) to produce a weight for each molecule. If we take the limiting case where all molecules are stationary then it should be easy to convince yourself that at some depth within the fluid a given molecule has a force acting upon it purely from gravity $Mg$ [$M$ is the molecules mass] plus the weight of all those molecules above it $\Sigma_{i}m_{i}g$ [where $m_{i}$ is the mass of the ith molecule], but also a reaction force provided by the contact with the molecule directly below it $R$, where

$$R = Mg + \Sigma_{i}m_{i}g,$$

for some arbitrary stationary molecule. From this it should be clear that the absolute force acting on this molecule (in the vertical direction, for our ideal column) increases with the depth of the molecule. This is essentially what causes pressure in a fluid, in increases the fluid density with depth.

Note. Of course the above is very much simplified as there will be much more going on at the molecular level, but this example should provide you with a basic Newtonian view with which to build from.

I hope this helps.

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In short: because the weight does it so.

Imagine a situation where several people are walking on each other in a small room: those that are at the top don't feel any discomfort whereas those at the bottom are crunched by the weight of the one above them. It's quite the same for the molecules.

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So you mean to say , they have to hit the upper molecules harder, those molecules who are more deep ? –  user23503 May 8 '13 at 8:28
@nonagon I would rather think it the other way around: top molecules hit bottom one harder because they are also falling (and then gaining speed) in the gravitational potential. Newton's third law (action/reaction) finishes: those on the bottom have to push harder in order for the top one not to fall to the ground. –  JJ Fleck May 8 '13 at 11:33
But temperature increases with depth ? So , one can say energy increased in terms of Kinetic Energy and that increased the speed and impact caused by the lower molecules . –  user23503 May 8 '13 at 12:58