- #1

ollien

- 6

- 0

## Homework Statement

That pressure is equal at all the same height no matter the shape of the container.

## Homework Equations

[itex]P = \frac{F}{A}[/itex]

[itex]P = ρgh[/itex]

## The Attempt at a Solution

I'm trying to understand this from my physics class, but I can't seem to get a hold on it. Why does pressure in water only depend on the height? I can understand that pressure at a depth is caused by the weight of the water on top of it, as shown by [itex]P = \frac{F}{A}[/itex]

Now, I know that the following is also true. [itex]P = ρgh[/itex] Now, this equation shows directly that it is related to height, and it can also be rearranged to [itex]P = \frac{F}{A}[/itex]. However, this is where to start to run into issues.

Let's say we have a cylindrical container of fluid, like so.

This cylinder, filled with fluid, will have a pressure on the bottom. Now, let's assume we have a conular container, with the same height, and equal base area, like so.

From my knowledge of [itex]P = ρgh[/itex], I know that the pressures are equal at the base. However, I can't begin to understand why. There is a lower volume of water in the cone, and therefore a lower mass. This means that there's a lower force pressing down from the water than in the cylinder. Because of this, shouldn't there be two different gauge pressures? What's the reasoning for there being equal gauge pressures? I can't begin to figure it out for the life of me.

Thanks so much.