EXPERIMENT (2)

BUOYANCY & FLOTATION(METACENTRIC HEIGHT)

Name enrollment no.Dipen Trivedi 140170119061Keval Trivedi 140170119062Keval Vadhediya 140170119063Dhaval Vadher 140170119064

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ARCHIMEDES’ PRINCIPLE

Archimedes’

Principle

statesthat

thebuoyantforce has a magnitude equal to the weight of

thefluiddisplaced

bythe

bodyand

isdirectedvertically upward.

• Buoyant force is a force that results froma

floating or submerged body in a fluid.• The force results from different pressures on

thetop and bottom of the object.

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ARCHIMEDES’ PRINCIPLE

The force of the fluid is vertically upward and isknown as the Buoyant Force (Upthrust Force).

The force is equal to the weight of the fluidit

displaces. The buoyantforcesacts through the centroid

ofthe displaced volume

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The location is known as the center of buoyancy.

STABILITY: SUBMERGED OBJECT

Stable Equilibrium: if when displaced returns to equilibrium position. Unstable Equilibrium: if when displaced it returns to a new equilibriumposition.Stable

Equilibrium:Unstable Equilibrium:

C > CG, “Higher”

C < CG, “Lower”

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STABILITY: SUBMERGED OBJECT

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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.

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

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If M lies above G a righting moment is produced, equilibrium is stable and GM is regarded as positive.

produced, equilibrium is unstable and GM If M lies below G an overturning

moment isisregarded as

negative. the body is inneutral

If M coincides withG, equilibrium.

Stable

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Unstable

DETERMINATION OF METACENTRIC HEIGHT1- Theoretically:

MG = BM + OB – OG

In Water

OB = 0.5

V

10of the

body

b.d

OG = Centre of Gravity from the bottom surface

h

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Find V from Archimedes’ Principlemg=V ρ g, so V = m/ρwhere:

m is the total mass of pontoonρ is the density of water

DETERMINATION OF METACENTRIC HEIGHT

2- Practically :

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PURPOSE:

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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.

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

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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

PROCEDURE

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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 thebottom 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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