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
Image
Courtesy: Google
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