EXPERIMENT (2)

BUOYANCY & FLOTATION

(METACENTRIC HEIGHT)

By:

Eng. Motasem M. Abushaban.

Eng. Fedaa M. Fayyad.

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ARCHIMEDES’ PRINCIPLE

Archimedes’ Principle states that the buoyant

force has a magnitude equal to the weight of the

fluid displaced by the body and is directed

vertically upward.

• Buoyant force is a force that results from a

floating or submerged body in a fluid.

• The force results from different pressures on the

top and bottom of the object.

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ARCHIMEDES’ PRINCIPLE

The force of the fluid is vertically upward and is

known as the Buoyant Force (Upthrust Force).

The force is equal to the weight of the fluid it

displaces.

The buoyant forces acts through the centroid of

the displaced volume

The location is known as the center of buoyancy.

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STABILITY: SUBMERGED OBJECT

Stable Equilibrium: if when displaced returns to equilibrium position.

Unstable Equilibrium: if when displaced it returns to a new equilibrium

position.

Stable Equilibrium: Unstable Equilibrium:

C > CG, “Higher” C < CG, “Lower”4

STABILITY: SUBMERGED OBJECT

If the Centre of Gravity is below the centre of

buoyancy this will be a righting moment and the

body will tend to return to its equilibrium

position (Stable).

If the Centre of Gravity is above the centre of

buoyancy ,an overturning moment is produced

and the body is (unstable).

Note that, As the body is totally submerged, the

shape of displaced fluid is not altered when the

body is tilted and so the centre of buoyancy

unchanged relative to the body.5

BUOYANCY AND STABILITY: FLOATING OBJECT

Slightly more complicated as the location of the center buoyancy can change:

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METACENTRE AND METACENTRIC HEIGHT

Metacentre point (M): This point, about which

the body starts oscillating.

Metacentric Height (GM) : Is the distance

between the centre of gravity of floating body and

the metacentre.

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STABILITY OF FLOATING OBJECT

If M lies above G a righting moment is produced,

equilibrium is stable and GM is regarded as

positive.

If M lies below G an overturning moment is

produced, equilibrium is unstable and GM is

regarded as negative.

If M coincides with G, the body is in neutral

equilibrium.

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Stable

Unstable

DETERMINATION OF METACENTRIC HEIGHT

1- Theoretically:

MG = BM + OB – OG

OG = Centre of Gravity from the bottom surface

of the body

In Water

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OB = 0.5 db

V

.

h

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Find V from Archimedes’ Principle

mg=V ρ g, so V = m/ρ

where:

m is the total mass of pontoon

ρ is the density of water

DETERMINATION OF METACENTRIC HEIGHT

2- Practically :

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PURPOSE:

To determine the metacentric height of a flat

bottomed vessel in two parts:

PART (1) : for unloaded and for loaded pontoon.

PART (2) : when changing the center of gravity of

the pontoon.

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EXPERIMENTAL SET-UP:

The set up consists of a small water tank having

transparent side walls in which a small ship

model is floated, the weight of the model can be

changed by adding or removing weights.

Adjustable mass is used for tilting the ship,

plump line is attached to the mast to measure

the tilting angle.

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PROCEDURE

PART (1) : Determination of floatation characteristic for

unloaded and for loaded pontoon:

1. Assemble the pontoon by positioning the bridge

piece and mast.

2. Weigh the pontoon and determine the height of

its center of gravity up the line of the mast.

3. Fill the hydraulic bench measuring tank with

water and float the pontoon in it, then ensure

that the plumb line on the zero mark.

4. Apply a weight of 50 g on the bridge piece

loading pin then measure and record the angle of

tilting and the value of applied weight

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PROCEDURE

5. Repeat step 4 for different weights; 100, 150, &

200 g, and take the corresponding angle of tilting.

6. Repeat the above procedure with increasing the

bottom loading by 2000 gm and 4000 gm.

7. Record the results in the table.

8. Calculate GM practically where , W has three

cases.

9. Draw a relationship between θ (x-axis) and GM

(y-axis), then obtain GM when θ equals zero.

10. Calculate GM theoretically.

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Bilge

Weight

Off balance

wt.

Mean

Def.

Exp.

GM

GM at

θ =0BM OB

Theo.

GM

Wb (gm) P (gm)θ

(degree)(mm)

from

graph(mm) (mm) (mm)

0.00 50

100

150

200

2000.00 50

x1 = 30 100

150

200

4000.00 100

x1 = 37.5 150

200

250

Pontoon measurement:

- Pontoon dimension : Depth (D) = 170 mm

Length (L) = 380 mm, Width (W) = 250 mm.

-The height of the center of gravity of the pontoon is OGvm = 125 mm from

outer surface of vessel base.

- The balance weight is placed at x = 123 mm from pontoon center line.

- The weight of the pontoon and the mast Wvm = 3000 gm

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QUESTIONS