# Relationship between centre of buoyancy and gravity

### Metacentric height - Wikipedia

The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its When a ship heels, the centre of buoyancy of the ship moves laterally. It might also . The metacentre has a direct relationship with a ship's rolling period. Centre of Buoyancy is defined as a point through which the buoyancy is supposed to act. It is same as the centre of gravity of fluid displaced by the body. In physics, buoyancy or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of gravity defining a "downward" direction. The center of buoyancy of an object is the centroid of the displaced volume of fluid.

To understand how the center of gravity behaves relative to center of buoyancy imagine a pendulum constructed from a rotating joint, and a stick connecting the rotating joint to a weight at the other end of the stick - the pendulum 'bob'.

• Differentiate Centre Of Gravity, Centre Of Buoyancy And Metacentre?
• Metacentric height

The weight is the ship's center of gravity, and the pivot point is the ship's center of buoyancy. If you start with the bob directly over the center of rotation center of gravity over center of buoyancy and just give it a small nudge, the pendulum will move away from the nudge and go through a large swing so that the bob eventually comes to rest below the center of rotation. If however you start with the bob directly below the center of rotation center of gravity below center of buoyancy and then give it a small nudge you will feel the pendulum push back towards the nudge, attempting to maintain it's lower position.

The first case - the 'inverted' pendulum is 'unstable'. The latter case, the pendulum as we normally see it, is 'stable'. Compressible objects[ edit ] As a floating object rises or falls, the forces external to it change and, as all objects are compressible to some extent or another, so does the object's volume.

Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands. If an object at equilibrium has a compressibility less than that of the surrounding fluid, the object's equilibrium is stable and it remains at rest.

If, however, its compressibility is greater, its equilibrium is then unstableand it rises and expands on the slightest upward perturbation, or falls and compresses on the slightest downward perturbation. To dive, the tanks are opened to allow air to exhaust out the top of the tanks, while the water flows in from the bottom. Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth.

Most military submarines operate with a slightly negative buoyancy and maintain depth by using the "lift" of the stabilizers with forward motion. As a balloon rises it tends to increase in volume with reducing atmospheric pressure, but the balloon itself does not expand as much as the air on which it rides. The average density of the balloon decreases less than that of the surrounding air. The weight of the displaced air is reduced. A rising balloon stops rising when it and the displaced air are equal in weight.

Similarly, a sinking balloon tends to stop sinking.

Divers[ edit ] Underwater divers are a common example of the problem of unstable buoyancy due to compressibility. The diver typically wears an exposure suit which relies on gas-filled spaces for insulation, and may also wear a buoyancy compensatorwhich is a variable volume buoyancy bag which is inflated to increase buoyancy and deflated to decrease buoyancy.

### Differentiate Centre Of Gravity, Centre Of Buoyancy And Metacentre? | Mecholic

The desired condition is usually neutral buoyancy when the diver is swimming in mid-water, and this condition is unstable, so the diver is constantly making fine adjustments by control of lung volume, and has to adjust the contents of the buoyancy compensator if the depth varies. This section does not cite any sources. January Density column of liquids and solids: If the fluid has a surface, such as water in a lake or the sea, the object will float and settle at a level where it displaces the same weight of fluid as the weight of the object.

If the object is immersed in the fluid, such as a submerged submarine or air in a balloon, it will tend to rise. If the object has exactly the same density as the fluid, then its buoyancy equals its weight.

This is converted to potential energy by raising the centre of mass of the hull with respect to the water level or by lowering the centre of buoyancy or both. This potential energy will be released in order to right the hull and the stable attitude will be where it has the least magnitude. It is the interplay of potential and kinetic energy that results in the ship having a natural rolling frequency. These are gravity acting downwards at the centre of mass and the same magnitude force acting upwards through the centre of buoyancy, and through the metacentre above it.

The righting couple is proportional to the metacentric height multiplied by the sine of the angle of heel, hence the importance of metacentric height to stability.

## Metacentre

As the hull rights, work is done either by its centre of mass falling, or by water falling to accommodate a rising centre of buoyancy, or both. For example, when a perfectly cylindrical hull rolls, the centre of buoyancy stays on the axis of the cylinder at the same depth. However, if the centre of mass is below the axis, it will move to one side and rise, creating potential energy. Conversely if a hull having a perfectly rectangular cross section has its centre of mass at the water line, the centre of mass stays at the same height, but the centre of buoyancy goes down as the hull heels, again storing potential energy.

When setting a common reference for the centres, the molded within the plate or planking line of the keel K is generally chosen; thus, the reference heights are: Beyond that range, the stability of the vessel is dominated by what is known as a righting moment.