Lab Stability of Floating Bodies

Group / Section 02

Lecturer DR. NURRINA BINTI ROSLI

Date Conducted 21 SEPTEMBER 2018

Lab Location THERMAL-FLUID LAB

Lab Objectives

To Design And Conduct One Experiment In Determined The Stability

Of Floating Bodies In Stable And Unstable Equilibrium At Various

Heights.

MARKS

REPORT

TEAM

ASSESSMENT

Student ID Name Signature

FB13040 IZZAT KHAIRI BIN MUHAMMAD KAMIL

HA15016 AHMAD FAHIM AFIQ BIN JAMALUDIN

FA15077 NOR AKMAL BIN ABD AZIZ

FA17057 NUR DIANA FARHANA BINTI ZULKIFLEE

FB17084 WAN RASYIQAH BINTI WAN HAIRUDDIN

35

15

Objectives :

To design and conduct one experiment in determined the stability of floating bodies

in stable and unstable equilibrium at various heights.

Theory :

The total weight that act through centre of gravity should be same to buoyancy force

that also act through centre of buoyancy which is located at centre of immersed

cross section.The Metacentre will identified as the point of intersection between line

of action of buoyancy force which is always be in vertical and buoyancy gravity is

extended.when the pontoon heels through a small angle. Metacentre must be above

the gravity to get a stable equilibrium.

Section through floating pontoon

The centre of gravity and the centre of buoyancy will move to its new position when

the inclining weight moved to one side. The angle of tilt ? is small will assume to

considering the stability of floating body. The theory can be simplified by making an

assumption ? radian = sin ? = tan ? = ? radian. First equation can be determined by

the depth of centre of buoyancy of height of metacentre above the buoyancy and

second moment of inertia can be determined using another equation considering the

restoring moment that rights a rectangular pontoon to an even keel when it is tilted.

BM ? I ws /V

Depth of immersion of pontoon = V/ l b

Centre of buoyancy, CB = V/2 l b

Methods :

1. The inclining weight moved to the centre of pontoon, measured by 0mm on linear

scale and tighten the securing screw.

2. Pontoon floated in the water and the immersed depth d for comparison measured

with the calculated value.

3. The inclining weight was traversed to the right in 15mm increments until the end

of the scale and the angular of displacement (?) of the plumb line for every position

of the weight noted.

4. Traversing the inclining weight to the left of the centre was repeated with the same

procedure.

5. Position of pontoon centre of gravity changed by moving the sliding weight up to

the mast.

6. Evaluated the lower position with the weight at the bottom of the mast.

7. Keep repeating the test and the metacentric height was determined for each new

position of G.

Results :

37.5cm

* All units already convert to SI units

Vertical

distance of

CG (m)

Horizontal distance (m)

0.06 0.04 0.02 -0.02 -0.04 -0.06

Angle of tilt from the vertical rod (rad)

0.0275 0.1745 0.1484 0.0785 -0.0698 -0.1309 -0.1745

0.0775 0.2094 0.1571 0.0698 -0.0349 -0.0698 -0.1047

0.1000 0.1486 0.1221 0.0349 -0.1309 -0.2007 -0.2440

Table 1: The angle observes in the different CG height

Vertical

distance of

CG (m)

Horizontal distance (m)

0.06 0.04 0.02 -0.02 -0.04 -0.06

Metacentric height, Hm (m)

0.0275 0.0296 0.0232 0.0218 0.0245 0.0262 0.0296

0.0775 0.0247 0.0219 0.0245 0.0491 0.0491 0.0491

0.1000 0.0347 0.0281 0.0491 0.0131 0.0172 0.0213

Table 2: The Metacentric height, Hm (m)

X

Graph of angle of vertical rod vs vertical distance of CG

Floating body:

Length, L = 0.3500m

Width, W = 0.2000m

Height of Sides = 0.0800m

Overall Rod Height = 0.3800m

Weight:

All the body, m = 2.15kg

Horizontal sliding weight, mh = 0.184kg

Vertical sliding weight, mv = 0.462kg

Center of Gravity

Xs (from center) = 0m

Zs (from the underside) = 0.075m

Calculations :

Metacentric height:

(1)

Where;

m = mass of adjustable weight (kg)

mp= mass of pontoon (kg)

= displacement of weight

= measured angle of list (radian)

By using the equation (1) to calculate metacentric height

= 0.0296m

Conclusion :

A floating body is said to be stable at its position, if it returns to that position following

a small disturbance. The experiment demonstrates how the stability of a floating

body is affected by changing the height of its centre of gravity and how the

metacentric height may be established experimentally by moving the centre of

gravity sideways across the body.

Throughout this experiment we made it to determine the metacentric height and

varying the metacentric height with angle of heel. By using various heights as shown

in the results, we determine the stability of floating bodies in stable and unstable

equilibrium.

As the lateral position of weight curve been added, the value of angle of list increase.

This make the floating bodies become unstable from time to time. The vale

established in this way agrees satisfactorily with that given by analytical result

BM=I/V.

Application In Industry :

1. Stability Of Ships

a) Intact Stability

– When the intactness of its hull is maintained on the stability of a

surface ship, and no compartment or watertight tank is damaged or

freely flooded by seawater.

– Types of equilibrium conditions that can happen

i. Stable Equilibrium

A stable equilibrium is achieved when vertical position of G is

less than the position of transverse metacentre (M). As the ship

follows to an angle (theta – ?), the center of buoyancy (B) is

shifted to B1. For the result of this condition, the ship will back to

its original position.

Righting Moment is when the ship is the result of uprighting to its original

orientation. The Righting Lever is the lever that causes the righting of a ship is the

separation between the vertical lines passing through G and B1,

and abbreviated as GZ.

ii. Neutral Equilibrium

It occurs when the vertical position of CG coincides with the

transverse metacentre (M). As shown in image below, no

righting lever is generated at any angle of heel. As the result,

heeling moment will not rise to righting moment and ship will

remain in heeled positions as long as neutral stability strong

enough. The larger the angle of heel in stable shift, the higher

risk an unwanted weight shift due to cargo shifting might cause

unstable equilibrium.

Neutral Equilibrium

iii. Unstable Equilibrium

As the vertical position of G is bigger than the position of

transverse metacenter (M) an unstable equilibrium happens.

When the ship tilts to an angle (say theta- ?), the center of

buoyancy (B) now shifts to B1. But the righting lever is now

negative and created further tilts until a stable equilibrium.

Unstable Equilibrium

The stability of the ship is depends on GM ;-

GM > 0 means the ship is stable.

GM = 0 means the ship is neutrally stable.

GM < 0 means the ship is unstable.

Reference :

1. STABILITY OF A FLOATING BODY. (n.d.). Retrieved September 24,2018,

from https://user.engineering.uiowa.edu/~cfd/pdfs/57-020/stability.pdf

2. Chakraborty, S. (2017). Ship Stability – Understanding Intact Stability of

Ships. Naval Architecture, Retrieved September 25, 2018, from

https://www.marineinsight.com/naval-architecture/intact-stability-of-surface-

ships/

3. FLUID MECHANICS LABORATORY. (n.d.). Retrieved September 24,2018,

from https://www.scribd.com/document/265632442/Experiment-2-Stability-of-

Floating-Body

4. Mechanics of Fluids and Transfer Processes Laboratory Experiment #2,

STABILITY OF A FLOATING BODY

https://user.engineering.uiowa.edu/~cfd/pdfs/57-020/stability.pdf

5. Stability of a Floating Body, TecQuipment Ltd 2015

http://cste.sut.ac.th/miscste/company/manual/H2.pdf