FACULTY OF PETROLEUM AND RENEWABLE ENERGY ENGINEERING

UNUNIIVVEERRSSIITITI TTEKEKNNOLOGIOLOGI MAMALLAYAYSSIIAA

FFLLUUIIDD MMEECCHHANANIICCSS LLAABOBORARATOTORRYY

TITLE OF EXPERIMENT

STABILITY OF FLOATING BODY (E 2)

Name MUHAMMAD KHAIRIL IKRAM(A13KP0047)

AKMAL FAIZ BIN ABDUL RAHIM (A13KP0008)

ABDUL WAHAB (A13KP4006)

KSATRIYA ANANTAYUTYA (A13KP4001)

Group / Section 1/Section

Supervisor Associate Professor Issham bin Ismail

Date of Experiment 3/3/2014

Date of Submission 9/3/2014

Marks obtained (%)

REPORT SUMMARY

The report is prepared for the sake of discussing about the principle in fluid mechanics which is the

stability of floating body which relates to the concept of centre of gravity and the location centre of

buoyancy. The appropriate location these two are matters since they will determine whether or not

a random floating body is either stable or not when placed in water. By theory, we know that when

the centre of buoyancy point of the body is higher/same than the centre of gravity, hence the body

is in neutral stability while if the case is opposite, otherwise will happen. Hence, the experiment is

conducted to prove this theory and according to the analysis prepared ,the theory is proven to be

correct.

INTRODUCTION

Laboratory experiment 2 is an exercise in hydrostatics. It is designed to demonstrate the stability

of a floating cylinder and to familiarize the student with the concept of buoyancy, metacenter, and

metacentric height. It is also an experimental verification of the theory presented in the textbook.

The center of the buoyancy (C, the centroid of the displaced volume of fluid) of a floating body

depends on the shape of the body and on the position in which it is floating. If the body is disturbed

by a small angle of heel, the center of buoyancy changes because the shape of the submerged

volume is changed. The point of intersection of the lines of action of the buoyancy force before and

after heel is called the metacenter (M) and the distance between the center of gravity (G) and M, is

called the metacentric height (GM,

PROCEDURE

. 1 The horizontal weight is taken out and the vertical weight is fixes on the mast of the pontoon

2. The thread is adjusted until it gives an angle of zero degree (no tilt).

3. The centre of gravity is determined by putting the pontoon mast on the mass balance. The

length of CG which is the length (in mm) is measured from the middle of mast to the base

pontoon.

4. The horizontal weight is fixed. The thread is made sure to be at zero mm (no tilt).

5. The tank is filled with water. Then, the pontoon is let to float in the tank.

6. Next, the length of the pontoon which was submerged in the water is measured.

7. After that, the horizontal weight is moved 10 mm to the right and the angle of tilt of the

thread is recorded.

8. The above step is repeated by using the horizontal weight 10 mm to the right. The angle of

tilt is recorded. This step is repeated until the plump bob which is hanging on the thread

touches the side of the pontoon.

9. The procedure is repeated by moving the horizontal weight to the left side.

10. The height of the vertical weight is adjusted to new height and procedures no. 7, 8, and 9

are repeated. The test is done at two (2) values of vertical heights.

Theory :-

Symbols :-W = total mass of pontoon with the vertical weight (kg)w = mass of horizontal weight (kg)GM = height of meta-center (mm)θ = angle of tilt (degrees)x = distance by which the horizontal weight is moved (mm)I = second moment of water surface area at vertical axis (mm4)L = length of pontoon (mm)B = width of pontoon (mm)V = volume of displaced water (mm3)BM = length between center of body and meta-centery = the distance between the base of pontoon to the center of gravity

Given Data :-Mass of horizontal weight = 0.28078 kgTotal mass of pontoon with vertical weight = 1.16567 kgWidth of pontoon = 200 mmLength of pontoon = 350 mmHeight = 75 mm

If a horizontal weight is moved a distance “x” from the center, the pontoon will tilt. The angle of tilt can be measured by using the plumb bob.

Overturning couple, Co = wgxRighting couple, Cr = Wg(GM) tan θ

For equilibrium, Co = Cr then GM = wx / (W tan θ)

Calculation using area of second moment:-

BM = I/V, where I = LB3 /12 and V= W/

Thus, GM = BM – BG = BM – y + d/2

D a ta a nd R e sult:

  Movement To The Right

GM =wx / W tan θ

Movement To The Left

GM =wx / W tan θ

TESTS x (mm)θ

(degree)mm x (mm)

θ (degree)

mm

  10 2.5 55.17 10 3.5 39.38Test 01

20 5 58.06 20 5.5 50.03

  30 8.5 48.38 30 8.5 43.35CG = 128 mm

40 10.5 51.99 40 11 49.57

  50 13.6 50.17 50 13.5 50.17

              d = 19 mm

           

            

           

  10 2 67.98 10 2 68.98Test 02

20 4.5 61.21 20 4 63.9

  30 6.5 63.42 30 6 63.75CG = 117 mm

40 8 68.56 40 8 63.56

  50 10 68.3 50 10 63.3

  60 12 63 60 11.5 71.04 d = 21 mm

70 14 67.63 70 13.5 70.23

            

           

  10 1.5 91.99 10 1.5 91.99Test 03

20 2.5 110.34 20 3 91.9

  30 4 103.34 30 4 103.34CG = 75 mm

40 5.5 100.06 40 5.5 100.06

  50 7 93.09 50 7 93.09

  60 8.5 96.7 60 8.5 96.7 d = 23 mm

70 10 95.62 70 10 95.62

  80 11 99.14 80 11 99.14

Dis c ussion:

The purpose of this experiment was to study the static of floating body.

This is based on two concepts. The first is the ‘centre of gravity’ or CG, which is the effective

centre of the weight of all the elements comprising the body and the point through which the

total weight effectively acts. It does not change unless weight is changed or moved. Then there

is the ‘centre of buoyancy’ or CB, which is the geometric centre of the immersed part of the hull

of the body, and through which the buoyancy force effectively acts. It is continually moving as

the body heels or trims. A body is stable if, as the body moves, the CB generates a moment

sufficient to return the body to the upright.

Figure 1 shows that when the body is upright, the CG is directly above the CB, and so it will

remain stationary. If however the body is heeled by some external influence (eg: wind or waves)

the CB moves to one side, thus generating a restoring moment about the CG – see Figure 2. The

further the CB moves for a given heel angle, the greater the tendency to return to the upright. The

size of the ‘righting moment’ is the weight of the body multiplied by the distance GZ as shown

in

Figure 2, which is sometimes known as the ‘righting lever’.

If weights are moved to one side, so that the CG is no longer on the centreline, the body will

adopt a steady angle of heel so that the CG and CB are once again in the same vertical line – see

Figure 3.

One can also see from Figure 2 that the size of the righting moment crucially depends on the CG

height. Raising the CG inevitably reduces the stability. Conversely lowering the CG improves

the stability. But if this is achieved by adding ballast rather than lowering existing weights, it

reduces freeboard and may cause down-flooding through openings at lesser angles of heel.

It is clear, therefore, that the stability of a particular body is dependent on both the hull shape and

the amount and position of its component weights. Changes to either will also change the

stability characteristics. For this reason the basic design of the body dictates its stability

properties. The hull shape determines the way the CB will move. The layout, which determines

the position of most of the heavy components, limits to a large degree the extent to which the

overall CG can be controlled. The stability can then only be adjusted by carefully locating the

remaining components or adding ballast.

During the Expermint there are few key points to be noticed:

i. The water should come to an halt, i.e no wave motion. So that the readings are as

precise as possible.

ii. While measuring the angle, the bob seemed to have some frictional force with the

scale , hence it couldn’t move smoothly and give better measurements.

There are few circumstances that lead to error in the experiment.

1. The wave motion in the surface of the water. It was difficult to come to a point where the

wave motion stopped and then readings were taken, but there was still some wave motion

while the readings were being taken.

2. The angle measured using the tool was not giving precise values if the experimental step

was repeated. Thus, this shows the inaccuracy of the tool.

3. While measuring the distance of the pontoon base and the pontoon stabiliser, keeping

correct eye level for measuring the distance was difficult thus this lead to parallax error.

4. The Pontoon pole is not firmly connected to the pontoon thus sometimes it moves and

cause errors in the precision of the values of the angle of tilt.

GM

(mm

)Graph:

70

Test 1: Movement to the right

60

50 y = -0.6196x + 57.723R² = 0.4902

40

30

20

10

00 2 4

D6egree(

8

θ)

10 12 14 16

GM

(mm

)Test 1: Movement to the left

60

y = 0.7827x + 39.92550 R² = 0.4162

40

30

20

10

00 2 4 6 8 10 12 14 16

Degree(θ)

GM

(mm

)Test 2: Movement to the right

69

68

67

y = 0.1072x + 64.855

66 R² = 0.0216

65

64

63

62

61

600 2 4 6 8 10 12 14 16

Degree(θ)

GM

(mm

)Test 2: Movement to the left

72

71

70

69

y = 0.3021x + 64.02168 R² = 0.1266

67

66

65

64

63

620 2 4 6 8 10 12 14 16

Degree(θ)

GM

(mm

)115

Test 3: Movement to the right

110

105

100

y = -0.49x + 101.85R² = 0.0815

95

900 2 4 6 8 10 12

Degree(θ)

GM

(mm

)104

Test 3: Movement to the left

102

100

98 y = 0.3144x + 94.495R² = 0.0665

96

94

92

900 2 4 6 8 10 12

Degree (θ)

Conclusion:

From this experiment, we can made three conclusions. Firstly, the position of meta-centric, M

for the body is changing according to the position of the body gravity center. Secondly, the

position of meta-centric, M is also changing according to the angle, θ. Next, the location of

meta-center is change according to the tilt angle and inversely proportional to the tilt angle. The

meta-centric position, M is linear to 1/θ. The position of meta-center will change according to

the angle from the equation,

Meta-centric position,

The position of meta-center of the body is linear with 1/ θ, in which when the value of θ

becomes smaller, the value of GM become greater and it is the same for the opposite situation.

Reference:

Rolf H. Sabersky, Allan J Acosta, Edward G. Hauptmann and E.M. Gates, "Fluid Flow-A First

Course of Fluid Mechanics" (Fourth Edition), Prentice Hall Inc., 1999.

5.Monsun B. R. Fundamentals of Fluid Mechanics. USA :John Wiley & Sons, Inc, 1994.

R.V Giles, “Fluid Mechanics and Hydraulics” (Third Edition), McGrawHill Inc; 1994.

Lab Manual University Teknologi Malaysia.

4.Robert A. Granger. ‘Experiments in Fluid Mechanics’.Holt, Rinehart and Winston, Inc. NewYork. 1988.

Appendices

LIST OF SYMBOLS

B Center of buoyancy

B’ Displaced center of buoyancy

d Transverse distance of displacement of added mass

FB Buoyancy force or upthrust

G Center of gravity of floating body

G’ Displaced center of gravity of floating body

G1 Displaced center of gravity of floating body with free surface

GZ Moment arm of restoring couple

g Acceleration due to gravity

IOy Second moment of area of plane of floatation about its longitudinal axis

i Second moment of area for free surface tank

K Keel

KOy Mass radius of gyration of floating body about its longitudinal axis

M Transverse metacenter

m Mass

T Period of oscillation

W Weight of floating body

Greek Symbols:

Angle of heel or inclination

Density of seawater

f Density of liquid in tank

Calculation Example:

To get height of meta-center (mm), we use the equation,

GM = wx / W tan θ ,

w = 0.28078 kg

W= 1.16567 kg

x = 10.0 mm ( taken from Test 01 movement to the right)

θ = 1.50 o

Then,

GM = (0.28078 kg x 10 mm) / (1.16567 kg x tan 1.50 o)

= 91.9862 mm

This calculation has been repeated to gain a data as stated in schedule.