# FLUID MECHANICS # ------------------------------------------------------------------------------------- BUOYANCY AND FLOTATION ------------------------------------------------------------------------------------- CONTENT ------------------------------------------------------------------------------------- > BUOYANT FORCE > CENTRE OF BUOYANCY > ARCHIMEDES PRINCIPLE > METACENTRE AND METACENTRIC HEIGHT > EQUILIBRIUM OF FLOATING AND SUBMERGED BODIES ------------------------------------------------------------------------------------- CREATIVE SLIDES

2. FLUID MECHANICS

3. BUOYANCY AND FLOTATION

4. C O N T E N T
▪ Buoyant force
▪ Centre of Buoyancy
▪ Archimedes Principle
▪ Metacentre and Metacentric height
▪ Equilibrium of floating and submerged bodies

5. WHAT IS BUOYANT FORCE?
BUOYANTFORCE
When an object is placed in a fluid, the
fluid exerts an upward force on that object, this
force is known as the buoyant force.

6. DIRECTION OF BUOYANT FORCE
BUOYANTFORCE
▪ Because the pressure increases as the depth
increases, the pressure on the bottom of an
object is always larger than the force on the top -
hence the net force is in upward direction.

7. DIFFERENT CONDITIONS
BUOYANTFORCE
▪ If the buoyant force is greater than the
object's weight, the object will rise to the
surface and float.
▪ If the buoyant force is less than the object's
weight, the object will sink.
▪ If the buoyant force equals the object's
weight, the object will remain suspended at
that depth.

8. WHAT IS CENTRE OF BUOYANCY?
CENTRE
OFBUOYANCY
The centre of buoyancy of an object is
an imaginary point through which the buoyant
force is considered to act.

9. LOCATION CENTRE OF BUOYANCY
CENTRE
OFBUOYANCY
▪ The centre of buoyancy of a vessel or object
is:
• Within its underwater shape
• Located at the centroid of the underwater
shape
CB

10. STATEMENT
ARCHIMEDES
PRINCIPLE
“ Whenever a body is immersed wholly or
partially in a fluid it is lifted up by a force equal to
the weight of fluid displaced by the body.”

11. DIFFERENT CONDITIONS
ARCHIMEDES
PRINCIPLE
▪ If the weight of the water displaced is less
than the weight of the object, the object will
sink.
▪ If the weight of the water displaced is equal
to the weight of the object, the object will
float.

12. FORMULA
H
h
b
W
G
B
FB
BODY
L I Q U I D
G = Centre of gravity of body
B = Centre of buoyancy
▪ Consider a body partially submerge in a liquid density 𝜌 as shown in
figure given below.
▪ The body is subjected to following two forces:
1. Downward gravitational force (W)
2. Upward force of liquid (FB)

13. FORMULA
H
h
b
W
G
B
FB
BODY
L I Q U I D
G = Centre of gravity of body
B = Centre of buoyancy
▪ The upward force of liquid is known as force of buoyancy (FB) and is equal to
weight of water displaced by body.
▪ FB = weight of water displaced by body
= 𝜌*g*volume of water displaced by body
= 𝜌*g*(h*b*l)

14. METACENTRE
METACENTREAND
METACENTRICHEIGHT
Whenever a body floating in liquid, is given a
small angular displacement, it starts oscillation about a
point. This point, about which body starts oscillation is
called Metacentre.

15. METACENTRE
METACENTREAND
METACENTRICHEIGHT
▪ Metacentre is intersection of line passing through the
original centre of buoyancy and centre of gravity of the
body, and vertical line passing through the new centre
of buoyancy.

16. METACENTRIC HEIGHT
METACENTREAND
METACENTRICHEIGHT
“Metacentric height is the distance between
the centre of gravity of a floating body and
its metacentre.”
The distance GM is called metacentric height.

17. METACENTRIC HEIGHT
METACENTREAND
METACENTRICHEIGHT
▪ The metacentric height (GM) is a measurement of
the initial static stability of a floating body.
▪ A larger metacentric height implies greater initial
stability against overturning.

18. STABILITY OF FLOATING BODY
EQUILIBRIUMOFFLOATING
ANDSUBMERGEDBODIES
▪ The stability of floating body is determine by the
location of its centre of gravity(G) and
metacentre(M).
▪ There are three types of equilibrium of floating body.
1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium

19. ▪ CONDITIONS:
• W = FB
• M is above G
▪ If the floating body is given small angular
displacement in clockwise direction, then the centre
of buoyancy shifts from B to B1.
▪ The buoyant force FB through B1 and W produce a
couple acting in a anticlockwise direction.
▪ Hence floating body returns in its original position.
▪ So, floating body is said to be in stable equilibrium.
STABLE EQUILIBRIUM
W
G
B
FB

20. ▪ CONDITIONS:
• W = FB
• M is below G
▪ If the floating body is given small angular
displacement in clockwise direction, then the
buoyant force FB through B1 and W produce a
couple acting in a clockwise direction.
▪ Hence floating body will overturn.
UNSTABLE EQUILIBRIUM
W
G
B
FB
M
G
U N S TAB L E P O S I T I O N

21. ▪ CONDITIONS:
• W = FB
• M and G at same point
▪ If the floating body is given small angular
displacement in any direction, there is no any
couples produces due to W and FB, since W and
FB are acting at the same point .
▪ So, floating body is said to be in neutral
equilibrium.
NEUTRAL EQUILIBRIUM
W
G
B
FB
M
G
N E U T R AL P O S I T I O N

22. STABILITY OF SUBMERSED BODY
EQUILIBRIUMOFFLOATING
ANDSUBMERGEDBODIES
▪ For a body totally immersed in a fluid, the position of
centre of gravity(G) and centre of buoyancy(B) of
body are fixed.
▪ The stability of submersed body is determine by the
location of G and B.
▪ There are three types of equilibrium of submersed
body.
1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium

23. ▪ CONDITIONS:
• W = FB
• G is below B
▪ If the submersed body is given small angular
displacement in clockwise direction, then the W and
FB not on the same vertical line.
▪ So, they produce a couple acting in a anticlockwise
direction.
▪ Hence submersed body returns in its original
position.
▪ So, floating body is said to be in stable equilibrium.
STABLE EQUILIBRIUM
W
G
B
FB

24. ▪ CONDITIONS:
• W = FB
• G is above B
▪ If the submersed body is given small angular
displacement in clockwise direction, then the W and
FB produce a couple acting in a clockwise
direction.
▪ Hence body does not returns to its original position
and body is said to be in unstable equilibrium.
UNSTABLE EQUILIBRIUM
W
G
B
FB

25. ▪ CONDITIONS:
• W = FB
• G and B at same point
▪ If the submersed body is given small angular
displacement in any direction, there is no any
couples produces due to W and FB, since W and
FB are acting at the same point .
▪ So, floating body is said to be in neutral
equilibrium.
NEUTRAL EQUILIBRIUM
W
GB
FB

26. THANK YOU