Simple question about water pressure in a cylinder

In summary, the conversation discusses the pressure in a vertical cylinder filled with water and how it differs on the sides compared to the bottom. The pressure on the sides is determined to be p_0+\rho g z, while the pressure downwards is calculated to be L*g*rho. The concept of pressure being the same in all directions for a liquid is mentioned and the conversation ends with the realization that there may be a lack of understanding in fundamental physics.
  • #1
leviadam
9
0
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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  • #2
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]
 
  • #3
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.
 
  • #4
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"
 
  • #5
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.
 

1. What is water pressure?

Water pressure is the force exerted by water against the walls of its container or any object in its path. It is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2).

2. How does water pressure change in a cylinder?

Water pressure in a cylinder depends on the depth and volume of water in the cylinder. As the depth of water increases, the weight of the water above it also increases, resulting in higher pressure. Similarly, as the volume of water decreases, the pressure increases due to the same amount of weight acting on a smaller area.

3. What is the formula for calculating water pressure in a cylinder?

The formula for calculating water pressure in a cylinder is P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of water.

4. How does water pressure affect objects in a cylinder?

Water pressure can affect objects in a cylinder by exerting a force on them. This force can either push objects towards the bottom of the cylinder or keep them afloat, depending on the density and volume of the object. The higher the water pressure, the greater the force exerted on the objects.

5. How can water pressure be measured in a cylinder?

Water pressure in a cylinder can be measured using a pressure gauge or a manometer. These devices measure the force exerted by the water against a certain area and display it in units of pressure. Alternatively, water pressure can also be calculated using the formula mentioned in question 3.

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