Conceptual Question About Hydrostatic Forces

[theLiminator]

Homework Statement

A 30-ft-high, 1-ft-diameter pipe is welded to the top of a cubic container (3ft x 3ft x 3ft). The
container and pipe are filled with water at 20°C. Determine the pressure forces on the bottom and sides of the container.

I already know the solution to this problem, but I don't get how it conceptually makes sense. It says that the pressure at the bottom would be equal to 33ft*specific weight of water. However, I don't get this concept. It basically means the amount of water on top makes a difference to the pressure at the bottom, only the height. My questions is, if you change the diameter of that pipe to something ridiculously small, such as 1 micron, why would the pressure at the bottom remain unchanged?

 

[theLiminator]

Oh, another concept I don't get:

If we attached a steel hollow sphere with a very thin thickness to the bottom, and remove to top tube, the pressure would go down right? But imagine if you add an ultra thin, but really long tube to the top, and fill that tube with water, wouldn't it crush the sphere due to incredibly high pressure? To me this isn't intuitive if you end up only adding maybe 500g of water (when using an incredibly thin tube).

 

[WeMade]

Aren't the units of pressure (force by area) like psi. So you'll have the same pressure with the same height of water because pressure is independent of the actual area.
You're just saying that this much force is acting per this area (which is a constant).
This makes sense to me, I hope its right and hope it helped.

 

[method_man]

My questions is, if you change the diameter of that pipe to something ridiculously small, such as 1 micron, why would the pressure at the bottom remain unchanged?

As far as I know it should be. Try to google and find something about Pascal's Vases or hydrostatic paradox.

 

[DeeNos]

The pressure at the bottom of the container is determined by the weight of the water above it, not the diameter of the pipe. This means that even if the diameter of the pipe is reduced to 1 micron, the weight of the water above it would still be the same and therefore the pressure at the bottom would remain unchanged. The diameter of the pipe does not affect the weight of the water and therefore does not impact the pressure at the bottom of the container.