## Saturday, 24 February 2018

We were discussing the basic definition of Buoyancy or buoyancy force, Centre of buoyancy, analytical method to determine the meta-centric height and conditions of equilibrium of submerged bodies in our previous posts.

Today we will see here the conditions of equilibrium of floating bodies with the help of this post.

### Conditions of equilibrium of floating bodies

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

Stability of a floating body will be dependent over the position of meta-centre. Before going ahead, we must have to find the detailed post about the basic concept of Meta-centre and Meta-centric height.

We must note it here that in case of floating body, weight of the body will be equal to the weight of the liquid displaced. Let us consider a floating body as displayed here in following figure.

### Stable equilibrium

Floating body will be considered in stable equilibrium condition, if following criteria will be fulfilled.
Meta-centre (M) should be above the centre of gravity (G).

Let us assume that we are giving an angular displacement to body in clockwise direction. Centre of buoyancy will be shifted to B1 from B as displayed in above figure.

Line of action of buoyancy force passing through this new position will intersect the normal axis passing through the centre of gravity and centre of buoyancy in original position of the body at a point M as displayed here in above figure. Where, M is the meta-centre.

Weight W and buoyancy force FB will now form one couple and this couple will tend to move the body in anti-clockwise direction. Hence, this couple will tend to move the body to its original position.

Stable equilibrium condition of the floating body is displayed here in above figure (a).

### Un-stable equilibrium

Body will be considered in unstable equilibrium condition; if meta-centre (M) is below than the centre of gravity (G). Unstable equilibrium condition of the floating body is displayed here in above figure (b).

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

### Neutral equilibrium

Body will be considered in neutral equilibrium condition, if meta-centre M and centre of gravity G are at same point.

We will discuss another topic i.e. Lagrangian method and Eulerian method in our next post.
Do you have any suggestions? Please write in comment box.

### Reference:

Fluid mechanics, By R. K. Bansal