Buoyancy and floatation

BUOYANCY AND FLOATATION

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ALAY MEHTA 141080106011SHIVANI PATEL 141080106021KAVIN RAVAL 141080106026KUNTAL SONI 141080106028

FLUID MECHANICS [F.M.]

BUOYANCY AND FLOATATION BUOYANCY 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 the overlying fluid.

Thus the pressure at the bottom of a column

of fluid is greater than at the top of the column.

BUOYANCY AND FLOATATION Similarly, the pressure at the bottom of an

object submerged in a fluid is greater than at the top of the object.

This pressure difference results in a net upwards force on the object.

The magnitude of that force exerted is

proportional to that pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid.


BUOYANCY AND FLOATATION For this reason, an object whose density is

greater than that of the fluid in which it is submerged tends to sink.

If the object is either less dense than the liquid or is shaped appropriately , the force can keep the object afloat.

This can occur only in a reference frame which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction .


In a situation of fluid statics, the net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body.

Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 B.C. For objects, floating and sunken, and in gases as well as liquids , Archimedes' principle may be stated thus in terms of forces:


With the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.

More tersely: Buoyancy = weight of displaced fluid.

Archimedes' principle does not consider the surface tension (capillarity) acting on the body, but this additional force modifies only the amount of fluid displaced, so the principle that Buoyancy = weight of displaced fluid remains valid.

BUOYANCY AND FLOATATION Assuming Archimedes' principle to be

reformulated as follows,

Then inserted into the quotient of weights, which has been expanded by the mutual volume:


The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes.:

.


Fb = P A = g ρ V = ρ g h A ..........................(a)

Here, P = pressure

Fb = force of buoyancy in Newton,A = Area in meter square,g = acceleration due to gravity, h = Height at which force acts taken from the surface,ρ = density of the fluid, V = volume of the object inserted into the fluid.


Fb = Wa – Wf .....................(b)

Where, Fb is the buoyant force

Wa = The Normal weight of the object when it is in air,Wf = The Apparent weight of the object when it is in the immersed in the fluid.


Hence using (a) in (b)

g ρ V = Wa – Wf ..........................(c)

So volume or

V = Wa–Wf / gρ .................(d)


And putting it in the formula for density we get:

ρ = Wa–Wf / gV ..........................(e)

If the object is not sinking then Fg = Fb

mg = ρ v g .......................................(f)


Neutral Buoyancy

Neutral Buoyancy is a situation in which the body immersed in the fluid will just float. It will neither rise nor sink.


A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement.

For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up.


Rotational stability is of great importance to floating vessels.

Given a small angular displacement, the

vessel may return to its original position (stable), move away from its original position (unstable), or remain where it is (neutral).



Rotational stability depends on the relative lines of action of forces on an object.

The upward buoyancy force on an object acts through the center of buoyancy, being the centroid of the displaced volume of fluid.

The weight force on the object acts through its center of gravity.


Buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment'.

The stability of a buoyant object at the surface is more complex, and it may remain stable even if the centre of gravity is above the centre of buoyancy, provided that when disturbed from the equilibrium position, the centre of buoyancy moves further to the same side that the centre of gravity moves, thus providing a positive righting moment.

If this occurs, the floating object is said to have a positive metacentric height.


This situation is typically valid for a range of heel angles, beyond which the centre of buoyancy does not move enough to provide a positive righting moment, and the object becomes unstable.

It is possible to shift from positive to negative or vice versa more than once during a heeling disturbance, and many shapes are stable in more than one position.

Buoyancy and floatation

Engineering