Short Notes: Stability of Floating Bodies | Short Notes for Mechanical Engineering PDF Download

 Page 1


Stability of Floating Bodies
Stability of Submerged Body: It is classified into the three groups.
• Stable Equilibrium: When centre of buoyancy lies above the centre of gravity, 
submerged body is stable.
• 6
•G
Stable equilibrium
• Unstable Equilibrium: When B lies below G , then body is in unstable 
equilibrium.
----------------------------.
•G
• B
Unstable equilibrium
• Neutral Equilibrium: When B and G coincide then, body is in neutral 
equilibrium.
B
G
Neutral equilibrium
Stability of Floating Bodies: When the body undergoes an angular displacement 
about a horizontal axis, the shape of the immersed volume changes and so the
Page 2


Stability of Floating Bodies
Stability of Submerged Body: It is classified into the three groups.
• Stable Equilibrium: When centre of buoyancy lies above the centre of gravity, 
submerged body is stable.
• 6
•G
Stable equilibrium
• Unstable Equilibrium: When B lies below G , then body is in unstable 
equilibrium.
----------------------------.
•G
• B
Unstable equilibrium
• Neutral Equilibrium: When B and G coincide then, body is in neutral 
equilibrium.
B
G
Neutral equilibrium
Stability of Floating Bodies: When the body undergoes an angular displacement 
about a horizontal axis, the shape of the immersed volume changes and so the
centre of buoyancy moves relative to the body.
• Stale Equilibrium: When a body is given a small angular displacement by 
external means and if body comes to its original position due to internal 
forces then, it is called stable equilibrium.
Stable position
It occurs, when metacentre lies above centre of gravity.
• Unstable Equilibrium: In the above case, if body does not come in its original 
position and moves further away then, it is known as unstable equilibrium. M 
lies below centre of gravity.
Unstable position
• Neutral equilibrium: When a body is given a small angular displacement and it 
sets on new position then, body is called in neutral equilibrium. In this, M and 
G coincide.
Neutral position
Relation between B,G and M is GM
V
Here, I = Least moment of inertia of plane of body at water surface 
G = Centre of gravity 
B = Centre of buoyancy 
M = Metacentre
G
Front view Top view
. . . w b d b d :
Page 3


Stability of Floating Bodies
Stability of Submerged Body: It is classified into the three groups.
• Stable Equilibrium: When centre of buoyancy lies above the centre of gravity, 
submerged body is stable.
• 6
•G
Stable equilibrium
• Unstable Equilibrium: When B lies below G , then body is in unstable 
equilibrium.
----------------------------.
•G
• B
Unstable equilibrium
• Neutral Equilibrium: When B and G coincide then, body is in neutral 
equilibrium.
B
G
Neutral equilibrium
Stability of Floating Bodies: When the body undergoes an angular displacement 
about a horizontal axis, the shape of the immersed volume changes and so the
centre of buoyancy moves relative to the body.
• Stale Equilibrium: When a body is given a small angular displacement by 
external means and if body comes to its original position due to internal 
forces then, it is called stable equilibrium.
Stable position
It occurs, when metacentre lies above centre of gravity.
• Unstable Equilibrium: In the above case, if body does not come in its original 
position and moves further away then, it is known as unstable equilibrium. M 
lies below centre of gravity.
Unstable position
• Neutral equilibrium: When a body is given a small angular displacement and it 
sets on new position then, body is called in neutral equilibrium. In this, M and 
G coincide.
Neutral position
Relation between B,G and M is GM
V
Here, I = Least moment of inertia of plane of body at water surface 
G = Centre of gravity 
B = Centre of buoyancy 
M = Metacentre
G
Front view Top view
. . . w b d b d :
V is volume submerged inside the water can be given as
V = bdx
Where b,d and x are the length, width and depth of the section or body.
S u b m e rg e d p a ri o f b o d y
BG is distance between centre of gravity and centre of buoyancy. (In other words, 
BG=distance between centre of gravity of whole body and centre of gravity of 
submerged part of body) When we find out GM then, we can determine the status 
of body as GM > 0 (stable equilibrium), GM < 0 (unstable equilibrium), GM = 0 
(neutral equilibrium).