CONDITIONS OF EQUILIBRIUM OF SUBMERGED BODIES

We were discussing the basic definition of Buoyancy or buoyancy force, Centre of Buoyancy, Meta-centre and meta-centric height and analytical method to determine the meta-centric height in our previous post. 
Today we will see here the conditions of equilibrium of submerged bodies with the help of this post.

Equilibrium of submerged bodies

A sub-merged or a floating body will said to be in equilibrium, if body will return back to its original position after giving a slight angular displacement or slight disturbance.

Stability of a submerged body will be dependent over the relative position of the centre of gravity i.e. G and centre of buoyancy B.

We must note it here that in case of completely submerged body, centre of gravity i.e. G and centre of buoyancy i.e. B will be fixed.

Let us consider a balloon completely submerged in air as displayed here in following figure. Let us assume that there will be heavy material of weight W at the lower portion of the balloon in order to maintain the centre of gravity below than the centre of buoyancy as displayed in following figure.

Weight W will act vertically downward through the centre of gravity G and buoyancy force F_B will act vertically upward through the centre of buoyancy as displayed in above figure.

Let us analyze the situation now. If W = F_B, balloon will be in equilibrium condition. Let us assume that we are giving an angular displacement to the balloon in clockwise direction. Weight W and buoyancy force F_B will now form one couple and this couple will tend to move the balloon in anti-clockwise direction. Hence, this couple will tend to move the balloon to its original position.

Stable equilibrium

Body will be considered in stable equilibrium condition, if following criteria will be fulfilled.

Weight W which is acting through the centre of gravity (G) should be equal to the buoyancy force F_B which is acting through the centre of buoyancy i.e. W = F_B

Centre of buoyancy i.e. point B must be above the centre of gravity G.

Stable equilibrium condition of the sub-merged balloon is displayed here in above figure (a).

Un-stable equilibrium

Body will be considered in unstable equilibrium condition; if weight W which is acting through the centre of gravity is equal to the buoyancy force F_B, but centre of buoyancy i.e. point B is below than the centre of gravity G. Unstable equilibrium condition of the sub-merged balloon is displayed above in figure (b).

Let us assume that we are giving an angular displacement to the balloon in clockwise direction. Weight W and buoyancy force F_B will now form one couple which will also act in clock direction. Therefore, balloon will not return back to its original position and therefore balloon will be in unstable equilibrium condition.

Neutral equilibrium

Body will be considered in neutral equilibrium condition, if weight W which is acting through the centre of gravity is equal to the buoyancy force F_B, but centre of buoyancy i.e. point B and centre of gravity G are at same point.

Neutral equilibrium condition of the sub-merged balloon is displayed above in figure (c). 

We will now understand the conditions of equilibrium of floating body.

Do you have any suggestions? Please write in comment box.

Reference:

Fluid mechanics, By R. K. Bansal

Image Courtesy: Google

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