flotation is much important to marine side

1. P R E S E N T B Y : -
• THM Elpitiya
• KH Maduranga

2. CONTENT…..
 Flotation
Properties of fluids
Archimedes' Principal
Vertical Moment
Calculation of Flotation

3. PROPERTIES OF FLUIDS
1.1 Distinction between a solid and a fluid
The molecules of a solid are usually closer
together than those of a fluid. The attractive forces
between the molecules of a solid are so large that a
solid tends to retain its shape. This is not the case for
a fluid, where the attractive forces between the
molecules are smaller

4. 1.2 Distinction between a gas and a liquid
A fluid may be either a gas or a liquid. The
molecules of a gas are much farther apart than those of a
liquid. Hence a gas is very compressible, and when all
external pressure is removed, it tends to expand
indefinitely.
A gas is therefore in equilibrium only when it is
completely enclosed. A liquid is relatively incompressible,
and if all pressure, except that of its own vapor pressure, is
removed, the cohesion between molecules holds them
together, so that the liquid does not expand indefinitely.
Therefore a liquid may have a free surface

6. 1.3 Specific volume
Is the volume occupied by a unit mass of fluid.
usually express it in cubic feet per slug (m3/kg in SI
units).
Specific volume is the reciprocal of density.
commonly apply it to gases.

7. Specific gravity s of a liquid is the dimensionless
ratio Physicists use 4°C (39.2°F) as the standard, but
engineers often use 60°F (15.56°C). In the metric system
the density of water at 4°C is 1.00 g/cm3 (or 1.00
g/mL),3equivalent to 1000 kg/m3 . density of a fluid varies
with temperature.

8. 1.4 Compressibility of liquids
The compressibility (change in volume due
to change in pressure) of a liquid is inversely
proportional to its volume modulus of elasticity,
also known as the bulk modulus.

9. This modulus is defined as
Ev = - v dp = - v dp
dv dv
where,
v = specific volume
p = pressure.
v/dv = dimensionless ratio,
The units of Ev and p are identical.

10. 1.5 Viscosity
The viscosity of a fluid is a measure of its
resistance to shear or angular deformation. The friction
forces in flowing fluid result from the cohesion and
momentum interchange between molecules.
How the viscosities of typical fluids depend on
temperature. As the temperature increases, the
viscosities of all liquids decrease, while the
viscosities of all gases increase.

12. 1.6 Surface tension
Liquids have cohesion and adhesion, both of
which are forms of molecular attraction.
Cohesion enables a liquid to resist tensile stress,
while adhesion enables it to adhere to another body.

14.  Archimedes Principle
Laws of flotation
Archimedes' Principle
states that when a body is
wholly or partially immersed
in a fluid it appears to suffer a
loss in mass equal to the
mass of the fluid it displaces.

15. Buoyancy
The “upward” force
acting on an object
due to the
displaced fluid
(such as water)
Archimedes’ Principle

16.  Vertical movement
Metacenter

17. Floating objects have a natural frequency like
a pendulum or metronome. That frequency is
determined (as with a metronome) by the amount
of mass on some length of swing arm being pulled
by gravity.
Greater mass or arm length means a slower
swing; and less mass or shorter arm length means a
faster swing.

18. The metacentre can be calculated using the formulae:
Where,
KB = centre of buoyancy,
I = Second moment of area of the waterplane
V = volume of displacement.
KM = distance from the keel to the metacentre.

19. Righting arm

20. They then calculate the righting moment at this angle
Where,
GZ is the righting arm
KB -to Centre of Buoyancy
KG - to Centre of Gravity
KMT - to Transverse Metacenter

21. Q & A