Meta-centric HeightAimTo determine the meta-centric height and
position of the meta-centric height using angle of heel and ship
model.
Apparatus Water Tank Weights of 1kg and half kg Ship model
(floating body)
TheoryMeta-centre is defined as the point about which a body
starts oscillating when the body is tilted by a small angle. The
meta- centre may also be defined as the point at which the line of
action of the force of buoyancy will meet the normal axis of the
body when the body is given a small angular displacement .It is
denoted by M. Meta-Centric Height is the distance between the
meta-centre (M) of a floating body and the centre of gravity (G) of
the body. Positive or negative value of Meta-centric height can
decide if the body will be in stable or unstable equilibrium.
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering
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Determination of Meta-centric Height Experimentally Let be the
weight of the Boat plus it's Load.
A small load is moved a distance and causes a tilt of angle .
The Boat is now in a new position of equilibrium with B1 and G1
lying along the Vertical through . The Moment due to the movement
of the load is given by = =
Hence, =
Where, W = weight of body including w G = centre of gravity of
body B = centre of buoyancy of the body M = meta-centre of the body
w = applied weight x = distance moved by weight w = angle of tilt
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 2
Procedure Fill tank with clean water Weigh the ship model to
find W. Float the ship model in water and ensure that it is in
stable equilibrium. Apply the known weight (w) at the center of
model. Give the model a small angular displacement in clockwise
direction. Measure the distance moved by the weight applied with
the help of scale. Measure the angle of tilt on the graduated arc
Repeat the experiment for different weights.
Observations Distance of grooves nos. 1, 2, 3, 4, from centre =
2.5 cm, 5 cm, 7.5 cm, 10 cm. Weight of ship model = 5.600 kg Weight
of big strip = 2.640 kg Weight of small strips = 1.110 kg (2 Nos),
Weight of hanger = 0.144 Kg Applied weights = 500 grams and 1000
grams w = Weight of hanger + applied weight W = Weight of ship
model + weight of big strip + weight of small strip + w
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering
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Observation tablesFor external weight = 500gm S. No. 1 2 3 4 5 6
7 8 Net w (kg) 0.644 0.644 0.644 0.644 0.644 0.644 0.644 0.644 W
(kg) 11.104 11.104 11.104 11.104 11.104 11.104 11.104 11.104
Distance(cm)=x 2.5 5.0 7.5 10 -2.5 -5.0 -7.5 -10 (degrees) 8 14 18
20 -6 -12 -17 -21 Meta-centric Height (cm) 1.032207 1.163683
1.339452 1.594336 1.380219 1.364988 1.423516 1.511716
For external weight = 1 kg S. No. 1 2 3 4 5 6 Net w (kg) 1.144
1.144 1.144 1.144 1.144 1.144 W (kg) 11.604 11.604 11.604 11.604
11.604 11.604 Distance(cm)=x 2.5 5.0 7.5 -2.5 -5.0 -7.5 (degrees)
24 29 33 -22 -29 -34 Meta-centric Height (cm) 0.55389 0.889814
1.139305 0.610369 0.889814 1.096918
Error Experiment has slight oscillations while taking the
readings. Manual checking of protractor
ConclusionMeta-centric height is calculated for different
loadings applied on floating body.
-Vrushiket Patil(09003044) Mechanical Btech 2009
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering
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