Simple question about water pressure in a cylinder

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Discussion Overview

The discussion revolves around the pressure exerted by water in a vertical cylinder, specifically focusing on the pressure on the sides of the cylinder compared to the pressure at the bottom. Participants explore the relationship between vertical pressure and lateral pressure in a liquid medium.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Adam poses a question regarding the pressure on the sides of a vertical cylinder filled with water, noting uncertainty about how it compares to the pressure downwards.
  • Another participant explains that the pressure at a depth z is given by the equation p_0 + ρgz, where p_0 is atmospheric pressure, and provides a calculation for the force on a small ring at that depth.
  • Adam questions whether the pressure acting downwards is the same as the pressure acting on the sides of the cylinder, expressing doubt about the reasonableness of this assumption.
  • A later reply suggests that the requirement for pressure to be the same in all directions is a fundamental characteristic of liquids.
  • Adam acknowledges the discussion, reflecting on the learning experience despite having knowledge in advanced physics topics.

Areas of Agreement / Disagreement

Participants express differing views on whether the pressure on the sides of the cylinder can be considered the same as the pressure acting downwards, indicating that the discussion remains unresolved.

Contextual Notes

There is an implicit assumption that the behavior of liquids under pressure is uniform in all directions, but this is not universally accepted in the discussion.

leviadam
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Hi all,

I was asked today by a friend a simple question but couldn't answer so I'm asking you.
Let's assume we have a vertical cylinder full of water, what is the pressure on the sides of the cylinder?

If it was the pressure downwards it simply L*g*rho but to the sides I'm not sure...

10x a lot,
Adam.
 
Last edited:
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Hi.
The preassure in the cylinder on depth [tex]z[/tex] is [tex]p_0+\rho g z[/tex], where [tex]p_0[/tex] is an atmosphere.
The force exerting on a small ring with height [tex]dz[/tex] on depth [tex]z[/tex] inside the cylinder is:
[tex](p_0+\rho g z)2 \pi r dz[/tex]
For the whole cylinder this force is:
[tex]\int_0^L (p_0+\rho g z)2 \pi r dz=2 \pi r L (p_0 + \frac{1}{2}\rho g L)[/tex]
For the bottom of the cylinder the force is:
[tex](p_0+\rho g L)\pi r^2[/tex]
 
The force you have calculated is the force downwards.
I'm not sure it is the same answer for the sides of the cylinder.

How is it reasonable that the pressure downwards is the same as the pressure to the sides.

Adam.
 
leviadam said:
The force you have calculated is the force downwards.
I'm not sure it is the same answer for the sides of the cylinder.

How is it reasonable that the pressure downwards is the same as the pressure to the sides.

Adam.
The requirement that pressure be the same in all directions is pretty much part of the definition of "liquid"
 
Ah, now I get it.
It's funny, you can learn QFT and GR but you realize you sometimes have shortage in fundamental physics...

10q very very much.
 

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