# Simple question about water pressure in a cylinder

1. Jul 14, 2009

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,

Last edited: Jul 14, 2009
2. Jul 14, 2009

### physicsworks

Hi.
The preassure in the cylinder on depth $$z$$ is $$p_0+\rho g z$$, where $$p_0$$ is an atmosphere.
The force exerting on a small ring with height $$dz$$ on depth $$z$$ inside the cylinder is:
$$(p_0+\rho g z)2 \pi r dz$$
For the whole cylinder this force is:
$$\int_0^L (p_0+\rho g z)2 \pi r dz=2 \pi r L (p_0 + \frac{1}{2}\rho g L)$$
For the bottom of the cylinder the force is:
$$(p_0+\rho g L)\pi r^2$$

3. Jul 15, 2009

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.

4. Jul 15, 2009

### HallsofIvy

Staff Emeritus
The requirement that pressure be the same in all directions is pretty much part of the definition of "liquid"

5. Jul 15, 2009