Buoyancy

BUOYANCY:
    When a body is immersed in a fluid, an upward force is exerted by the fluid on the body. This upward force is equal to the weight of the fluid displaced by the body and is called the Force of Buoyancy or simply Buoyancy.
 The buoyant force is caused by the increase of pressure in fluid with depth.
 The buoyant force depends upon :
1.Density of fluid
2.Submerged Volume of the body.
 For a floating body in static equilibrium and in absence of any other external force, the buoyant force must balance the weight of the body.

 

Here the buoyant force is denoted by  and V is the Volume of the Submerged Body.

CENTRE OF BUOYANCY:

    Centre of Buoyancy is defined as the point through which the force of buoyancy is supposed to act. It is also defined as the  the center of mass of the fluid displaced by a floating or submerged body (such as a ship, submarine, or balloon). As the force of buoyancy is a vertical force and is equal to the weight of the fluid displaced by the body, the centre of buoyancy will be the centre of gravity of the fluid displaced.

For Better Understanding: Click Here

EXAMPLES :

Problem 1: Find the volume of the water displaced and position of centre of buoyancy fora wooden block of width 2.5 m and of depth 1.5 m, when it floats horizontally in water. The density of wooden block is 650 kg/ and its length 6.0 m.

Solution:

Given :
Width = 2.5m                                                                         

Depth = 1.5 m

Length = 6.0 m                                                                             

Volume Of the Block = 2.5*1.5*6.0 = 22.50  

Density of the wood,   = 650 Kg/

Therefore, Wight of block =  *g*Volume

                                          =650*9.81*22.50 N

                                          =143471 N

For equilibrium the weight of water displaced = Weight of wooden block

                                                                              = 143471 N

Volume of water displaced =  

Position of Centre of Buoyancy, Volume of wooden block in water

                                                      = Volume of water displaced

Therefore 2.5*h*6.0 = 14.625 , where h is the depth of the wooden block in water

h =  

Centre of Buoyancy =   from the base.

Problem 2: A stone weighs 392.4 N in air and 196.2 N in water. Compute the volume of stone and its specific gravity.

Solution :

Given:

Weight of stone in air = 392.4 N

Weight of stone in water = 196.2 N

For equilibrium,

Weight in air- Weight of stone in water = Weight of water displaced

392.4 - 196.2 = 196.2 = 1000*9.81*Volume of water displaced

Therefore Volume of water displced =    

                                                          

                                                              = Volume ofstone

Therefore,Volume of stone =

Specific Gravity of Stone 

Mass of stone =  

Density of stone =  

Hence Specific Gravity of stone =  

REFERENCE'S: 

1) Fluid Mechanics by Yunus A. Cengel, John M. Cimbala.

2) Fluid Mechanics And Hydraulic Machines by Dr R K Bansal.