We
were discussing the basic definition and derivation of total
pressure; centre
of pressure, buoyancy or buoyancy force and centre of buoyancy in our
previous posts.
Today
we will see here the basic concept of Meta-centre and meta-centric height with
the help of this post.
Meta-centre
Meta-centre
is basically defined as the point about which a body in stable equilibrium will
start to oscillate when body will be displaced by an angular displacement.
We
can also define the meta-centre as the point of intersection of the axis of
body passing through the centre of gravity and original centre of buoyancy and a
vertical line passing through the centre of buoyancy of the body in tilted
position.
Let
us consider a body which is floating in the liquid. Let us assume that body is
in equilibrium condition. Let us think that G is the centre of gravity of the
body and B is the centre of buoyancy of the body when body is in equilibrium condition.
In
equilibrium situation, centre of gravity G and centre of buoyancy B will lie on
same axis which is displayed here in above figure with a vertical line.
Let
us assume that we have given an angular displacement to the body in clockwise
direction as displayed here in above figure.
Centre
of buoyancy will be shifted now towards right side from neutral axis and let us
assume that it is now B1.
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.
Meta-centric height
Meta-centric
height is basically defined as the distance between the meta-centre of the
floating body and the centre of gravity of the body.
Therefore,
MG in above figure will be termed as meta-centric height.
Do
you have any suggestions? Please write in comment box.
Reference:
Fluid mechanics, By R. K. Bansal
Image
Courtesy: Google
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