Please explain the concept of Buoyancy and Flotation.with examples?

Buoyancy and flotation

When a body floats in a static fluid, the vertical forces acting on it are in equilibrium.  If it is displaced upwards a small distance, the hydrostatic force supporting it (its buoyancy) is decreased so that the upward force is now less than the body's weight.  There is thus a net downward force which tends to return the body to its original position.  Similarly, if the body is initially displaced downwards a small distance, the forces go out of equilibrium and set up a resultant upward force which tends to restore the original position again.  Such a body has vertical stability.

Assuming that the fluid is of constant density, the upwards buoyancy force on any submerged object must act at the centroid of the fluid displaced.  This point is called the Centre of Buoyancy.  The weight of the object acts downwards at its Centre of Mass - and that does not necessarily coincide with the Centre of Buoyancy.  The rotational stability of any body floating or submerged in a fluid actually depends on whether the rotational "couple" set up by the weight and buoyancy acting at these two points when the body is tilted tends to return it to its original position (rotationally stable) or tends to overturn it (rotationally unstable).



Totally submerged body

Consider the forces acting on a small submersible vessel designed with a low centre of mass:  if it experiences a small angular displacement, then the couple set up tends to restore the vessel to its original orientation - and it is stable.  Note that only if a fully submerged vessel has its centre of mass above its centre of buoyancy will it be unstable.



Floating vessels



   



Floating vessels frequently have their centre of mass above the centre of buoyancy - but most of them remain stable.  This is because the centre of buoyancy moves horizontally as the floating vessel tilts, thereby again producing a couple which tends to restore the vessel to equilibrium.  The point M where the line of action of the buoyancy force of the tilted vessel meets the line through the centre of mass G which was originally vertical is known as the metacentre, and the distance between the centre of mass and the metacentre, GM, known as the metacentric height. This is of particular importance to Naval Architects interested in the stability of ships, as the restoring moment is equal to [mg GM sinØ].