Buyouncy is the force exerted on a body from the fluid it is immersed in. For example placing a sphere in water, causes a buyouncy force from the water to the sphere upwards. Even air exerts this force to things in it.
It works like this. In fluids, we can measure the pressure at any point. Imagine a Square Cube with a length of "h" on each of its faces, immersed in a pool of water with the top and bottom face, horizontal. Because of the difference of height of "l" between it's top and bottom surface there is a total net force of Buyouncy=A*(Pbottom - Ptop) [where A=l*l is the face area]. We are able to calculate the pressure as "P=water density*g*h" where g=gravity and h=depth we shall have:
Buyouncy=l*l*water density*g*(hbottom-htop)
Since it is a square cube l*l*(hbottom - htop)=Volume
Therefor we have "Buyouncy=water density*g*V"
If the fluid in which the body is immersed in is not water, the density used is the density of the fluid. So we shall have: Buyouncy=density*g*V
It can be proved that even if the body immersed in the fluid is not a cube, the above formula is correct.
