system
Given the following post, respond as if you're commenting on Reddit:
human
Suppose there is an upright cylinder completely submerged in water. Since the top of the cylinder is higher then the bottom, shouldn't there be more pressure on the bottom and thus an upwards force on the cylinder?

I've been wondering about this for a long time. Why wouldn't the cylinder be pushed upwards? Suppose it has a total density that of water.
gpt
Yes. This is what causes the buoyancy of the object.

The vertical forces on the cylinder are gravity and the pressure forces on the top and bottom. The net pressure force is ρ*_0_*ghA, where ρ*_0_* is the density of water, h is its height, and A is the area of the circles that form its top and bottom. And the gravitational force is mg = ρgAh, where ρ is the density of the cylinder. Ah is just the volume of the cylinder (which also equals the volume of displaced water). 

So the condition for equilibrium between these forces is:

ρ*_0_*gV = ρgV, or ρ = ρ*_0_*.

To be neutrally buoyant in water, you need to have the same density as water. Objects with higher density will sink, and objects with lower density will float. And we call the vertical pressure difference force on a submerged object the “buoyancy force”, and it’s equal to the weight of the liquid displaced by the solid object. This is Archimedes’ law.