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Buoyancy, Buoyancy force & Centre of Buoyancy.

When a body is immersed in a fluid wholly or partially it is subjected to an upward force, which tends to

lift (or buoy) up the immersed body. This tendency for an immersed body to be lifted up in the fluid, due

to an upward force opposite to the action of gravity, is known as Buoyancy.

The force tending to lift up the body under such condition is known as Buoyancy force.The point of application of the force of buoyancy on the body is known as Centre of Buoyancy.

Magnitude of the Buoyancy Force.

The magnitude of the buoyancy force can be determined by the well knownArchimedes Principal,

which states that when a body is immersed in a fluid either wholly or partially it is buoyed or lifted up by

a force which is equal to the weight of the fluid displaced by the body.

i.e. the buoyant force is equal to the weight of the fluid displaced by the body.

Consider an elementary prism MN of cross-section dA out of the whole body on wholly submerged body

ABCD.

Since p > p

So elementary buoyant force (dF) = (pdA - pdA)

= (h - h)dA

or, dF = ydA = dV *dV = volume ofthe presume MN]

Total buoyancy force on the entire body

F = dV = V ----------------------(1)

Where, V = volume of the submerged body = vol. of displaced fluid.

Equation (1) shows that the buoyant force exerted on a

submerged body is equal to the weight of the fluid displace by

the body.

& weight of a body in liquid = weight of the body in air (W) () F ()

= weight of the body in air (W) () weight of displaced liquid ()

The buoyant force acts vertically upwards through the centre of buoyancy which coincides with the

centroid of the volume of the fluid displaced.

When a body floats at a surface of separation between two

immiscible fluids; then elementary buoyant force

dF = (pdA - pdA)

= *(hy) y - y+dA

= (y y)dA

= dV dVTotal buoyant force, (F) = dV dV

or, F = V V

Condition of Floatation

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For a body immersed (either wholly or partially) in a fluid, the self-weight of the body acts in the vertical

downward direction. As such if a body floating in a fluid is to be in equilibrium, the buoyant force must

be equal to the weight of the body.