UNIVERSITY OF ZIMBABWE

DEPARTMENT OF CIVIL ENGINEERING

NAME: DAWOOD SIYAYA

REG NUMBER: R176101Q

TOPIC: STABILITY OF A FLOATING BODY

DATE OF SUBMISSION: 17 APRIL 2018

TITLE:

STABILITY OF A FLOATING BODY

THEORY

Floating bodies are a special case; only a portion of the body is submerged, with the
remainder poking of the free surface. A floating object is stable as far as a resetting moment
exists in the event of deflection or tilting from the equilibrium position. As shown in Fig. 3,
dead weight and buoyancy form a force couple with the lever arm of , which provides a
righting moment. The distance between the centre of gravity and the point of intersection of
line of action of buoyancy and symmetry axis, is a measure of stability. The point of
intersection is referred to as the metacentre, , and the distance between the centre of gravity
and the metacentre is called the metacentric height. The figure below shows- Metacentre and
metacentric height.

OBJECTIVES:
1. To determine the centre of gravity of the pontoon.
2. To determine the metacentric height and from this the position of the metacentre for
the pontoon.
3. To investigate the stability of the pontoon by varying the angle of tilt

APPARATUS AND MATERIALS:

a) Bath of still water.
b) Metacentric height apparatus.
c) Metre rule.
d) Weighing balance.
 mast

Movable mass

Plumb line

Adjustable jockey mass

Rotation measurement

Pontoon

Water bath

EXPRIMENTAL PROCEDURE:
1. The external dimensions (length, breadth and depth) of the pontoon were
measured and recorded.
2. The transverse adjustable jockey mass was weighed separately and its mass was
recorded.
3. The transverse adjustable mass was then mounted onto the pontoon and the mass
of the entire assembly was determined and recorded.
4. The transverse adjustable mass was positioned at zero position on the transverse
scale.
5. The sliding mass was placed at the top most position of the mast.
6. The centre of gravity, G, was determined by balancing the pontoon mast on a knife
edge (the shorter side of the water basin)
7. The length GZ was measured and recorded.
 8. The datum for horizontal displacement of the transverse jockey mass was
determined by placing the pontoon in water and adjusting the transverse jockey
mass until there was zero rotation of the pontoon
9. Depth of immersion was determined by recording the distance (r) from the top of
the side of the pontoon to the water surface.
10. The transverse adjustable mass was moved to the right of the datum in 5mm
increments up to the end of the scale while the corresponding angular
displacements were recorded.
11. The whole procedure was repeated with the sliding mass on the mast positioned at
360mm and 300mm above the base of the pontoon.

OBSERVATIONS:
1. The following dimensions were measured and recorded as follows:
 Length of pontoon l = 350mm
 Breadth of pontoon b =200mm
 Depth of pontoon d = 75mm
 Mass of transverse jockey weight m = 408g
 Mass of entire assembly M = 1501.6g
 Depth from top of side of pontoon to water surface r =50mm
2. As the position of the sliding mass was being lowered from top of mast through
360mm to 330mm, respective sets of results also exhibited progressively lower
ranges of values of angular displacement.
3. The position of the centre of mass of the system lowered as the sliding mass was
also lowered.

EXPERIMENTAL RESULTS
1. The results of the experiment were tabulated as shown in Table 2 below

Experiment 1 (at the top) Experiment 2 (at 360mm) Experiment 3 (at 300mm)
𝑀𝑍 = 440𝑚𝑚 𝑀𝑍 = 300𝑚𝑚 𝑀𝑍 = 300𝑚𝑚
𝑀𝐺 = 320𝑚𝑚 𝑀𝐺 = 250𝑚𝑚 𝑀𝐺 = 205𝑚𝑚
𝐺𝑍 = 120𝑚𝑚 𝐺𝑍 = 50𝑚𝑚 𝐺𝑍 = 95𝑚𝑚
𝑟 = 50𝑚𝑚 𝑟 = 50𝑚𝑚 𝑟 = 50𝑚𝑚
dx(mm) dθ(o) dx(mm) dθ(o) dx(mm) dθ(o)
5 1 5 1 5 0.5
10 3 10 2.5 10 3
15 3.5 15 4 15 4
20 7 20 6 20 4.5
25 8 25 7 25 5.5
30 8.5 30 9.5 30 7
35 10.5 35 11 35 7.5
40 13.5 40 12.5 40 9
 45 14 45 10.5
50 14.5 50 11
55 12.5
60 13
65 14.5

Calculations:
Computation of MG from the rotation of the vessel

Metacentric height MG computed from measured rotation of the vessel;

𝑤 𝑑𝑥 𝑤 𝑑𝑥
MG = 𝑊* (𝑑𝜃 ) *57.3 = 𝑊* ( gradient of 𝑑𝜃 graph) *57.3

where:

w = transverse moveable jockey weight = 4.00N

W = total weight of the vessel = 14.73N

Experiment 1 Experiment 2
32.5−7 47−20.5
Gradient= = 3.04 Gradient= = 3.40
9.4−1 12−4.2

Experiment 3
50.5−21
Gradient= = 4.10
10.2−3

Set Number Metacentric gradient from Height (MG) (mm)

graph
1 3.04 38.26
2 3.40 42.79
3 4.10 51.60

Computation of MG from measured dimensions

Depth of immersion 𝑆 = 𝑑 − 𝑟 = 75 − 50 = 25𝑚𝑚

𝑆 25
Therefore 𝐵𝑍 = 2 = = 12.5𝑚𝑚
2

𝐼 𝑏×𝑏 200×200
Metacentre radius, 𝑀𝐵 = 𝑉 = = = 133.3𝑚𝑚
12𝑆 12×25
Metacentric height, 𝑀𝐺 = 𝑀𝐵 + 𝐵𝑍 − 𝐺𝑍

Set Number GZ(mm) MG(mm)

1 120 25.8
2 50 95.8
3 95 50.8

DISCUSSION OF RESULTS
1. The values of dx varied directly with the values of angular displacement at all positions
of the moveable mass on the mast
2. On the graph of GZ against experimental MG, values of GZ decreased with an increase
the values of MZ

SOURCES OF ERRORS
 Zero error. The setup reading isn’t zero at zero load.
 There were parallax errors in taking almost all measurements.
 Plumb line would hit the pontoon when trying to make it stable hence it would be
difficult to take readings
 The experiment was also carried out using faulty and very old instruments

PRECAUTIONS

 Extreme caution should to be taken in recording r.

 The readings should be taken when the apparatus come into equilibrium state to
minimise errors.
 Account for the zero were there was zero error before the reading are taken

CONCLUSIONS
 The stability of a vessel is affected adversely by the movement of the center of gravity
of the liquid in the tanks as the vessel heels (Douglas et al,2005). Thus the stability
was different depending on the position of G for the different experiments.
Experimental values vary slighltly from those calculated because of experimental
errors, some of them are :
 Parallax error when taking readings for angle of rotation
 Scale system error
 Pontoon is not exactly stable when measuring the volume of water displaced
 Whilst taking readings, the pontoon had to be guided so that it does not touch walls,
distorting the results
  From the graph GZ-MG metacenter M depends on centre of gravity G
 The y-intercept of the graph shows the neutral position where MG=0

REFERENCES

Roberson, J.A. and Crowe, C.T. (1993). Engineering Fluid Mechanics, 5th edition, Houghton
Mifflin, Boston, MA White, F.M. (1994). Fluid Mechanics, 3rd edition, McGraw-Hill, Inc.,
New York, NY

J. F. Douglas, J. M. Gasiorek, J. A. Swaffield and Lynne B. Jack Fluid Mechanics 2005

Pearson Education Limited ISBN-10: 0-13-129293-5 2.

Hewakandamby N.B, A First Course in Fluid Mechanics for Engineers, 2012, ISBN 978-87-
4030069-7