FLUID MECHANICS

1. BUOYANCY AND FLOATATION
-: CREATED BY :-
ALAY MEHTA 141080106011
SHIVANI PATEL 141080106021
KAVIN RAVAL 141080106026
KUNTAL SONI 141080106028
FLUID MECHANICS [F.M.]

2. BUOYANCY AND FLOATATION
 BUOYANCY is an upward force exerted by a fluid
that opposes the weight of an immersed object.
 In a column of fluid, pressure increases with depth
as a result of the weight of the overlying fluid.
 Thus the pressure at the bottom of a column of fluid
is greater than at the top of the column.

3. BUOYANCY AND FLOATATION
 Similarly, the pressure at the bottom of an object
submerged in a fluid is greater than at the top of the
object.
 This pressure difference results in a net upwards
force on the object.
 The magnitude of that force exerted is proportional
to that pressure difference, and is equivalent to the
weight of the fluid that would otherwise occupy the
volume of the object, i.e. the displaced fluid.

4. BUOYANCY AND FLOATATION

5. BUOYANCY AND FLOATATION
 For this reason, an object whose density is greater
than that of the fluid in which it is submerged tends
to sink.
 If the object is either less dense than the liquid or is
shaped appropriately , the force can keep the
object afloat.
 This can occur only in a reference frame which
either has a gravitational field or is accelerating due
to a force other than gravity defining a "downward"
direction .

6. BUOYANCY AND FLOATATION
 In a situation of fluid statics, the net upward
buoyancy force is equal to the magnitude of the
weight of fluid displaced by the body.
 Archimedes' principle is named
after Archimedes of Syracuse, who first discovered
this law in 212 B.C. For objects, floating and
sunken, and in gases as well as liquids ,
Archimedes' principle may be stated thus in terms
of forces:

7. BUOYANCY AND FLOATATION
 With the clarifications that for a sunken object the
volume of displaced fluid is the volume of the object,
and for a floating object on a liquid, the weight of the
displaced liquid is the weight of the object.
 More tersely: Buoyancy = weight of displaced fluid.
 Archimedes' principle does not consider the surface
tension (capillarity) acting on the body, but this additional
force modifies only the amount of fluid displaced, so the
principle that Buoyancy = weight of displaced fluid
remains valid.

8. BUOYANCY AND FLOATATION
 Assuming Archimedes' principle to be reformulated
as follows,
 Then inserted into the quotient of weights, which
has been expanded by the mutual volume:

9. BUOYANCY AND FLOATATION
 The density of the immersed object relative to the
density of the fluid can easily be calculated without
measuring any volumes.:
.

10. BUOYANCY AND FLOATATION
 Fb = P A = g ρ V = ρ g h A ..........................(a)
Here, P = pressure
Fb = force of buoyancy in Newton,
A = Area in meter square,
g = acceleration due to gravity,
h = Height at which force acts taken from the
surface,
ρ = density of the fluid,
V = volume of the object inserted into the fluid.

11. BUOYANCY AND FLOATATION
 Fb = Wa – Wf .....................(b)
 Where,
Fb is the buoyant force
Wa = The Normal weight of the object when it is in
air,
Wf = The Apparent weight of the object when it is in
the immersed in the fluid.

12. BUOYANCY AND FLOATATION
 Hence using (a) in (b)
 g ρ V = Wa – Wf ..........................(c)
 So volume or
 V = Wa–Wf / gρ .................(d)

13. BUOYANCY AND FLOATATION
 And putting it in the formula for density we get:
 ρ = Wa–Wf / gV ..........................(e)
 If the object is not sinking then Fg = Fb
 mg = ρ v g .......................................(f)

14. BUOYANCY AND FLOATATION
 Neutral Buoyancy
 Neutral Buoyancy is a situation in which the
body immersed in the fluid will just float. It will
neither rise nor sink.

15. BUOYANCY AND FLOATATION
 A floating object is stable if it tends to restore itself
to an equilibrium position after a small
displacement.
 For example, floating objects will generally have
vertical stability, as if the object is pushed down
slightly, this will create a greater buoyancy force,
which, unbalanced by the weight force, will push
the object back up.

16. BUOYANCY AND FLOATATION
 Rotational stability is of great importance to floating
vessels.
 Given a small angular displacement, the vessel
may return to its original position (stable), move
away from its original position (unstable), or remain
where it is (neutral).

17. BUOYANCY AND FLOATATION

18. BUOYANCY AND FLOATATION
 Rotational stability depends on the relative lines of
action of forces on an object.
 The upward buoyancy force on an object acts
through the center of buoyancy, being
the centroid of the displaced volume of fluid.
 The weight force on the object acts through
its center of gravity.

19. BUOYANCY AND FLOATATION
 Buoyant object will be stable if the center of gravity is
beneath the center of buoyancy because any angular
displacement will then produce a 'righting moment'.
 The stability of a buoyant object at the surface is more
complex, and it may remain stable even if the centre of
gravity is above the centre of buoyancy, provided that
when disturbed from the equilibrium position, the centre
of buoyancy moves further to the same side that the
centre of gravity moves, thus providing a positive
righting moment.
 If this occurs, the floating object is said to have a
positive metacentric height.

20. BUOYANCY AND FLOATATION
 This situation is typically valid for a range of heel
angles, beyond which the centre of buoyancy does
not move enough to provide a positive righting
moment, and the object becomes unstable.
 It is possible to shift from positive to negative or
vice versa more than once during a heeling
disturbance, and many shapes are stable in more
than one position.