# Buoyancy and Archimedes Principle

#### jot_dain

Hello all

I was hoping someone could help me with some intuition regarding Buoyancy and Archimedes Principle.

I thought i understood Buoyancy in terms of pressure but when i came across Archimedes Principle I realized I did not fully understand what Buoyancy is.

I have an object that is a cube 3 x 3 x 3 meters with a density of 900kg/m^3.

This object is submerged in water such that the top of the object is 15m below the surface and the bottom of the object is 18m below the surface.

I have calculated the pressure at the top & bottom of the object and since pressure increases with depth i knew the pressure at the bottom would be greater than the top.

So i thought that Buoyancy is the difference in pressure between the top and bottom of the submerged object and since the pressure was greater at the bottom then the fluid would want to push the object up to the surface.

I drew a diagram of my thinking:-

Based on the above my buoyancy force is the difference in pressure and in this case 2940.

However i have read about Archimedes Principle which states that the buoyancy force a submerged object experiences is equal to the weight of the fluid it displaces.

With this in mind I added the weight of the object due to gravity and included the buoyancy force the object would experience into my diagram to get:-

Factoring in Archimedes Principle i know that this object will float because the buoyancy force is greater than the weight of the object - the bit i am struggling to understand is how does the pressure at the top and bottom of the object get factored in this?

I hope this makes sense.

Can anyone shed any light?

Thank you.

#### Cervesa

hydrostatic force on a submerged object = pressure times surface area

downward force on the cube = (147150 Pa)(9 m^3) = 1324350 N

upward force on the cube = (176580 Pa)(9 m^3) = 1589220 N

buoyant force = upward force - downward force = 1589220 N - 1324350 N = 264870 N

weight of displaced water = 27(1000)(9.81) = 264870 N

note the buoyant force = weight of the displaced water
... this is Archimedes principle

weight of the object = (900)(27)(9.81) = 238383 N < the buoyant force, 264870 N ... the object will not sink.