Fluid Mechanics Applications/A:20 Stability and oscillation of floating bodies

INDRODUCTION
The aim of present work is to determine the stability and oscillation of a floating bodies which requires the basic knowledge of fluid statics like Archimedes principle of Buoyancy and states of equilibrium of a floating body.The various factors on which the stability and oscillation of a floating body depends will be discussed also to analyse things properly.

The equilibrium of floating or submerged bodies requires that the weight of the body acting through its centre of gravity has to be collinear with an equal buoyant force acting through the centre of buoyancy. A submerged body will be in stable ,unstable or neutral equilibrium if its centre of gravity is below, above or coincident with the centre of buoyancy respectively.

Stability of floating body depends on its metacentric height. Metacentre of a floating body is defined as the point of intersection of the centre line of cross section containing the centre of gravity and centre of buoyancy with the vertical line through new centre of buoyancy due to any smaller angular displacement of the body. The distance of metacentre from centre of gravity along the centre line of cross section is know as Metacentric height. For stable equilibrium of floating bodies,metacenter(M) has to be above the centre of gravity(G). Metacentre coinciding with centre of gravity or lying below refers to the situation of neutral and unstable equilibrium respectively.

A stable floating body subjected to small angular displacement by disturbances, such as waves, undergoes an oscillation of simple harmonic type.The time period of oscillation is inversely proportional to the square root of metacentric height. An increase in metacentric height results in a better stability at the cost of comfort due to a reduction in the time period of rolling.