Cc501 Buoyancy & Stability

7/24/2019 Cc501 Buoyancy & Stability

1/40

CC501-HYDRAULICS 2

CHAPTER 2BUOYANCY & STABILITY

HJ. ZAMALI BIN OMAR


2/40

BOUYANCY DEFINITIONS

The ability or tendency of a liquidto lift a body that is put into it

Keupayaan atau kecenderungansesuatu cecair untuk mengangkat

sesuatu badan yang diletakkan kedalamnya


3/40

INTRODUCTION

A fluid exerts a force on any object submerged in it.

Such a force due to a fluid in equilibrium is known

as the buoyancy or the upthrust.

It is often necessary to determine buoyancy in manyengineering applications as in the design of ships,

boats, buoys etc.


4/40

INTRODUCTION

The buoyancy has a magnitude equal to the weight

of the displaced olume of fluid.

It acts upwards through the centre of graity of thedisplaced olume of fluid which is known as the

centre of buoyancy.

This result is often known as the Archimedes

principle and can be proed as follows!


5/40

ARCHIMEDES PRINCIPLES

A body that is submerged orpartially submerged will

experience a buoyant force, inwhich the buoyant force is equalto the weight of the displaced

volume of liquid


6/40


"hen an object is submerged in a fluid in

equilibrium an equal olume of fluid is displaced.

This olume of fluid was in equilibrium under theaction of its own weight and the resultant thrust

exerted on it by the surrounding fluid which is the

same as the buoyancy on the submerged object.

#ence the buoyancy should be equal in magnitude

to the weight of the displaced olume of fluid and

act upwards through its centre of graity.


7/40



8/40



9/40


A body submerged or partially submerged in a fluid

will experience two $%& types of forces acting on the

body !

'.(raity force acting downward $"&%.)pthrust exerted by the fluid acting upward

$*&

+T-

If graity force / upthrust, body will

submerged

If graity force 0 upthrust, body will float


10/40

BUOYANCY

"hen a body is immersed in a fluid, an upward

force is exerted by the fluid on the body.

This upward force is equal to the weight of the fluid

displaced by the body and is called the force ofbuoyancy or buoyancy.


11/40

CENTRE OF BUOYANCY


12/40

CENTRE OF BUOYANCY

The position of the centre of buoyancy, 1 depends

on the shape of the displaced olume of fluid.

2or a fluid of uniform density, it is at the centroid ofthe displaced olume of fluid.

It should be distinguished from the centre of graity,( of the submerged object, the position of which

depends on the way its weight, " is distributed as

illustrated in 2igure 3.


13/40

CENTRE OF BUOYANCY


14/40

BODIES SUBMERGED IN TWO

IMMISCIBLE FLUIDS


15/40

BODIES SUBMERGED IN TWO

IMMISCIBLE FLUIDS


16/40

EXAMPLE 2.1

2ind the olume of the water displaced and position

of centre of buoyancy for a wooden block of width

%.4 m and of depth '.4 m when it floats hori5ontally

in water. The density of wooden block is 647 kg8m3

and its length 6.7 m.


17/40

SOLUTION


18/40

SOLUTION


19/40

EXAMPLE 2.2

Measuring 0!m wooden cubes"oating in water as shown below

#ood density is 0$ %eterminethe wooden block drafts&


20/40

EXAMPLE 2.3

The mass of a pontoon is '0metric tonnes (i)e or dimensions

pontoon is $m wide, *'m long +!m high #hat is the draft whenthe pontoon is loaded with *0

x*0,

kg of gravel The waterdensity is *0+'kg-m,


21/40

EXAMPLE 2.4

A rectangular pontoon is used totransport agricultural grain throughthe river #idth and length of each

pontoon is .'m and +/!m #ithoutload draft *'m #ith a load of grain,the draft is +*m %etermine&

i #eight of pontoon without loadii rains weight


22/40

STABILITY OF SUBMERGED

BODY


23/40


BODIES


24/40


BODIES


25/40

STABILITY OF SEMI-

SUBMERGED BODIES


26/40

STABILITY OF SEMI-

SUBMERGED BODIES


27/40

META-CENTER

The intersection of the ertical axis of a body when

in its equilibrium position 9 a ertical line throughthe new position of the 1' when the body is rotated

slightly.


28/40

LOCATION OF META-CENTRE


29/40

LOCATION OF META-CENTRE

MB = I / Vd

I : ;oment of inertia of a hori5ontal

section of the body taken at the surface

of the fluid


30/40

META-CENTRIC HEIGHT

The distance between the =-+T*- of (*A of

a floating body and the ;-TA?=-+T*- $distance;(&


31/40

META-CENTRIC HEIGHT

MG = MB +GB


32/40

EXAMPLE 1

A rectangular pontoon of 4 m long,

3 m wide and '.% m deep is immerse

7.@ m in sea water. If the density of

sea water is ''47 kg8m3, find the

meta?centric height of the pontoon.


33/40

SOLUTION


34/40

SOLUTION


35/40

EXAMPLE 1

A solid cylinder of % m diameter and

' m height has a mass of @77kg

floating in the water as in the figure.

2ind its meta?centric height and the

type of balance.


36/40

STEP 1

"eight of cylinder : "eight of water displaced

;g : gAd

@77 x B.@' : $'777&$B.@'&$C'%&d

d : $@77&8$'777&$C&

d : 7.%44 m


37/40

STEP 2

;( : ;1 D (1

;1 : I 8


38/40

STEP

;( : ;1 D (1

;( : 7.B@ m F 7.3H%4 m

: 7.67H4 m

=onclusion! Stable because ;( is De alue.


39/40

E!"#$%

A ship '0m long and .m wide weighing*'M1 A load of +00K1 moved 'm tothe right ship causing the ship tilted 0 2f

the center of buoyancy of the ship *'mbelow sea level, determine the metacentric position and center of gravityabove sea level


40/40

Documents

Cc501 Buoyancy & Stability