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ok so my friend told me that in a container, the pressure exerted by the walls on the liquid in the container act in the upward direction.Is he correct ? so what I am imagining is a cylindrical container kept on the ground. according to me the pressure by the wall of the container should act perpendicular to the surface of the wall.Am i going wrong somewhere ? Any help would be appreciated.

Karan Singh
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2 Answers2

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Pressure is a scalar and does not have a direction. This is discussed in some detail in the answers to Define Pressure at A point. Why is it a Scalar?, though this might be a bit technical.

When you measure a pressure you are actually measuring the force applied to a surface. For some small bit of surface $\delta {\bf A}$, the force produced on that surface due to a pressure $P$ is:

$$ \delta {\bf F} = P \delta {\bf A} $$

and the direction of the force is normal to the surface. So it's the orientation of the surface that determines the direction of the force.

We use small surface elements $\delta {\bf A}$ so that we can apply the formula to curved surfaces. Your particular case is a lot simpler, and you are basically correct. However note that when you say:

the pressure by the wall of the container should act perpendicular to the surface of the wall

Note that this should be:

the force by the wall of the container should act perpendicular to the surface of the wall

Community
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John Rennie
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  • I'm likely to be incorrect, but as far as I know, pressure is defined as compressive isotropic normal stress. By this definition pressure has direction sign (positive for compressive?) and a magnitude? Also, by this definition, it seems that pressure is defined as a special case of stress (simple stress situation). Also, if this is true, can fluid pressure be called fluid stress? My source: en.wikipedia.org/wiki/Stress_%28mechanics%29#Simple_stresses – Armadillo Oct 22 '14 at 21:08
  • @jake Yes. My answer to a spinoff of this question touches on this a little. –  Oct 23 '14 at 03:56
  • @ChrisWhite which part(s) of my comment are you saying yes to? Also, I will look at your spinoff question. I had posted a question that also touched on these matters as well. – Armadillo Oct 23 '14 at 12:19
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Pressure at a point in a static fluid is independent of direction.

http://www.southampton.ac.uk/~jps7/Aircraft%20Design%20Resources/Sydney%20aerodynamics%20for%20students/fprops/statics/node4.html

The force exerted by the walls on the liquid will be pointing inwards. Imagine if there is a hole in the container and water is liquid out, it is easy to see that you have to apply a force inwards in order to prevent the liquid from leaking. Since the force is proportional to the area of the hole, you'd want a dimensionally equivalent form of pressure in order to eliminate the dependence on area. And that is stress. (Note that stress is not a scalar nor a vector - it is a tensor)

http://en.wikipedia.org/wiki/Stress_(mechanics)

t.c
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  • Ok so what happens if the container is not cylindrical ? Suppose we take a container like a bucket ( frustum of a cone).will there be any upward force now? – Karan Singh Oct 22 '14 at 15:29
  • Yes since the force will have a Z component in addition to X and Y component, since the surface's normal is no longer in the XY plane but slightly tilted. – t.c Oct 22 '14 at 17:33