1. FLUID MECHANICS

2. CHAPTER ONE
1.1 INTRODUCTION TO FLUID
1.2 UNITS AND DIMENSION USED IN
ENGINEERING FLUIDS

3. INTRODUCTION
WHAT IS
HYDRAULICS
WHAT IS
FLUID
MECHANICS?
•Mechanics of fluids
•It’s that branch of engineering
science which deals with the
behaviour of fluid under the conditions
of rest & motion
•Greek word “HUDAR” , means –
“WATER”
•It’s that branch of engineering
science deals with water ( at rest or
in motion)
•Or its that branch of engineering
science which is based on
experimental observation of water
flow.

4. FLUID MECHANICS
FLUID MECHANICS is a study of the
behavior of liquids and gases either
at rest (fluid statics) or in motion
(fluid dynamics).
The analysis is  relate continuity
of mass and energy with force and
momentum.
FLUID is a substance which deforms
continuously under the action of
shearing force (however small it is
may be)

5. Last Updated:7 September 2022 © LMS SEGi education group 5
WHAT IS FLUID MECHANICS?
 Fluid – a substance that continually deforms (flows) under applied shear
stress
 Mechanics – science concerned with behaviour of physical bodies when
subjected to forces
 Fluid Mechanics – the science that deals with the behaviour of fluids at
rest (fluid statics) or fluids in motion (fluid dynamics), and their
subsequent effects on the surrounding environment

6. Application Areas of Fluid Mechanics

7. IMPORTANT OF FLUID MECHANICS
IMPORTANT
OF FLUID
MECHANICS
TO ENGINEER
To determine the
stability of floating and
submerged objects 
pontoons, ships
To determine the
hydrostatic forces 
dams
To determine flow and
energy losses in pipe
To design fluid
machines  pumps
and turbines
To determine flow
rate, energy
dissipation from
spillway and flow in
open channels such as
rivers

8.  Archimedes (285-212 BC) - buoyancy
 Blaise Pascal (1623-1662) - hydrostatics
 Daniel Bernoulli (1700-1782) – energy
equation
 Antonie Chezy (1718-1798) – velocity in
channel
 Henry Darcy (1803-1858) – groundwater
flow
 Jean Poiseuille (1799-1869) – laminar flow
 Lord Osborn Reynolds (1842-1912) – flow
regime
 Louis Navier (1785-1836), George Stokes
(1819-1903) – equations of fluid motion
with friction
 William Froude (1810-1879) – resistance
of partially submerged objects
 Lord Rayleigh (1842-1919) – 1-D flow
through constant area duct with heat
transfer
 Sir Horace Lamb (1849-1934) – waves in
solids
 Wilbur & Orville Wright – 1st aeroplane
 Ludwig Prandtl (1875-1953) – boundary
layer
Last Updated:7 September 2022 © LMS SEGi education group 8
HISTORY (Cengel & Cimbala, 2006)

9. Last Updated:7 September
2022
© LMS SEGi education group
9

10. DIFFERENCE BETWEEN SOLID AND FLUID
Have preferred
shape
Hard & not
easily
deformed
Cannot
deformed
continuously
under shear
force
SOLID
Does not have
any preferred
shape
Soft & easily
deformed
Deformed
continuously
under shear
force
FLUID
ITEM 1 ITEM 2

11. 3 CONDITIONS OF FLUIDS
• The study of
incompressible fluid
under static conditions
(hydrostatics)
• That dealing with the
compressible static
gases- aerostatics
STATICS
• Deals with the –
velocities,
accelerations and
pattern of flow only
• Force and energy
causing velocities and
accelerations are not
deal under this head.
KINEMATICS
• Deal with the
relationship between
velocities and
accelerations of fluid
with the FORCES @
ENERGY causing them.
DYNAMICS

12. CONCEPT OF FLUID
In FLUID:
-The molecules can move freely but are constrained through a traction force called
cohesion.
-This force is interchangeable from one molecule to another.
For GASES:
-It is very weak which enables the gas to disintegrate and move away from its container.
-A gas is a fluid that is easily compressed and expands to fill its container.
-It fills any vessel in which it is contained. There is thus no free surface.
For LIQUIDS:
-It is stronger which is sufficient enough to hold the molecule together and can withstand
high compression, which is suitable for application as hydraulic fluid such as oil.
-On the surface, the cohesion forms a resultant force directed into the liquid region and the
combination of cohesion forces between adjacent molecules from a tensioned membrane
known as free surface.

13. 1.1 FLUID AS CONTINUUM
Continuum mechanics and its concept
• It is a branch of mechanics that deals with the analysis
of the kinematics and mechanical behaviour of materials
modelled as a continuum. (eg. solids and fluids), (eg.
liquids and gases)
• A continuum concept assumes that the substance of the
body is distributed uniformly throughout, and
completely fills the space it occupies.
• Fluid properties is depends on their molecular
structure.However, engineering applications hardly
analyses fluids at molecular level.
• It is the fluid’s bulk behavior of main concern in
engineering applications.

14. CONTINUUM CONCEPTS
• Atoms are widely spaced in the gas
phase.
• However, we can disregard the
atomic nature of a substance.
• View it as a continuous,
homogeneous matter with no holes,
that is, a continuum.
• This allows us to treat properties as
smoothly varying quantities.
• Continuum is valid as long as size of
the system is large in comparison to
distance between molecules.

15. Fluid as a
continuum
• A continuous substance
where quantities such as
velocity and pressure can be
taken as constant at any
section irrespective of the
individual fluid particle
velocity.

16. PRESSURE
Pressure acts
perpendicular to the
surface and increases at
greater depth.
area
force
pressure 
Pressure is the force per unit area, where the force is perpendicular to the area.
 A measure of the amount of force exerted on a surface area

17. 1.2 UNITS AND DIMENSION USED IN ENGINEERING
FLUIDS
WHAT IS
UNITS?
WHAT IS
DIMENSION?
•Standardized system of
measurements used to
describe the magnitude of
the dimension
•A properties that can be
measured
•Measurable properties used to
describe a body/system
•The standard element, in terms of
which these dimensions can be
described quantitatively & assigned
numerical values.

18. VARIOUS SYSTEM OF UNIT
Parameter SI UNITS c.g.s system of unit
Imperial units ( British
Gravitational system; English
Units)
Length Meters (m) Centimeters (cm) Foot (ft)
Mass kilogram(kg) Gramme (g) Pound ( Ib)
Time Seconds (s) Seconds (s) Seconds (s)
Temperature Kelvin (K) Degree Fahrenheit ( oF)
• The primary quantities which are also referred to as basic dimensions, such as
L for length, T for time, M for mass and F for force.
• Student also expected to be familiar with the various systems of units used in
engineering. These systems include :
As any quantity can be expressed in whatever way you like it is sometimes easy to become confused
as to what exactly or how much is being referred to. This is particularly true in the field of fluid
mechanics.

19. DERIVED UNIT

21. 1. DENSITY
Regardless of form (solid, liquid,
gas) we can define how much mass
is squeezed into a particular space
Density of a material is defined by
the amount of matter per unit
volume.
Density of material may be
referred to in many ways.

22. 1.1 MASS DENSITY, 
Definition
Density of a fluid, , is defined as the mass per unit volume
• It is denoted by the Greek symbol, .
 ==
V m3
kgm-3
kg
m
 water= 1000 kgm-3
air =1.23 kgm-3

23. 1.2 SPECIFIC WEIGHT, 
Definition
Specific weight of a fluid,  , is defined as the weight of the fluid per unit
volume .
Force exerted by gravity, g, upon unit volume of substance
 =
w
V
= g
Units: N/m3
 = the density of the material (kgm-3)
g = acceleration due to gravity (ms-2)
 Water = 9.81 X 103 N/m3

24. 1.3 RELATIVE DENSITY
@ SPECIFIC GRAVITY, SG
Definition
A ratio of the specific weight of a substance to the specific weight of
water at standard temperature (4C) and atmospheric pressure.
Units: dimensionless
C
w
s
C
w
s
SG




4
@
4
@




Unit is none, since ratio is a pure number. SG is a dimensionless quantity

25. 2. SPECIFIC VOLUME, V
Definition
The reciprocal of the mass density i.e. the volume per unit mass or the
inverse of density
Units: m3/kg
v = 1/ = V/m

26. 3. VISCOSITY
Dynamic
Kinematic

27. 3.1 DYNAMIC VISCOSITY, µ
Definition
Dynamic viscosity, µ , is defined as the Shear force per unit area (shear
stress, ) needed to drag a layer of fluid with a unit velocity past another layer
at a unit distance away from it in the fluid
Measure of internal friction of fluid particles
•Molecular cohesiveness
•Resistance fluid has to shear (or flow)
Units:
Water:
Air:

28. 3.2 KINEMATIC VISCOSITY, ν
Definition
It defined as the ratio of dynamic viscosity to mass density
v



μ = dynamic viscosity
ρ= mass density
• Will be found to be important in cases
in which significant viscous and
gravitational forces exist.
Typical values:
Water = 1.14x10-6 m2/s;
Air = 1.46x10-5 m2/s;
Units: m2/s or stokes (10,000 St = 1m2s-1)

29. NEWTON LAW OF VISCOSITY
When fluid moves, it generates shearing stress
If no movement between the moving fluid particles  no shear stresses
developed
Fluid particles which in contact with solid boundaries will adhere to these
boundaries  will have same velocities as the solid boundaries
Movement of a fluid over solid boundary can be visualized as layers of a
fluid moving one above the other.
The velocity of fluid layers increases as the distance from the solid
boundary increases
y
v
Flowing passing over a solid boundary

30. TEMPERATURE VS VISCOSITY (LIQUID
AND GASES)
Liquids
Gases
Viscosity
Temperature
• Viscosity is caused by the cohesive
forces between the molecules in liquids
and by the molecular collisions in
gases, ant it varies greatly with
temperature.
• The viscosity of liquid decreases with
temperature, whereas the viscosity of
gases increases with temperature.
• This is because in a liquid the
molecules possess more energy at
higher temperature and they can
oppose the large cohesive
intermolecular forces more strongly.
• As a result, the energized liquid
molecules can move more freely.
• In gases, the intermolecular activities
are negligible and the gas molecules at
high temperature move randomly at
higher velocity.

31. VISCOSITY IN GASES & LIQUIDS
Viscosity in gases
• Due to intermolecular collision
between randomly moving particles
• For gas, temperature , amount of
intermolecular collision , viscosity
Viscosity in liquid
• Due to intermolecular collision
between liquid particles
• For liquid, temperature ,
intermolecular collision is weakened,
viscosity

32. NEWTON LAW OF VISCOSITY
 = shear stress (tau)
 = viscosity of fluid
du/dy = shear rate, rate of strain
or velocity gradient
dy
du

  (1.1)
• The viscosity  is a function only of the condition of the fluid, particularly its
temperature.
• The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .

33. NEWTONIAN &
NON NEWTONIAN FLUID
Fluid Newton’s law
of viscosity
Newtonian fluids
obey refer
Example: Air, Water, Oil, Gasoline, Alcohol, Kerosene, Benzene, Glycerine
Fluid Newton’s law
of viscosity
Non Newtonian fluids
not obey refer

34. NON NEWTONIAN FLUID
*The slope of a curve at a point is the apparent viscosity of the fluid at that point

35. 1.4 VAPOUR PRESSURE, SURFACE TENSION,
AND CAPILLARITY
At the end of this topic student should:
•Be able to define the fluid parameters.(CO1-PO1)
•Be able to apply surface tension and capillarity in solving fluid
engineering problem.(CO1-PO1)
•Be able to use the Newton’s law of viscosity which are the
relationship of shear stress and velocity gradient in solving fluid
engineering problems (CO1-PO3)

36. 4. SURFACE TENSION, σ
Surface tension
• defined as the force acting a unit length of
a line drawn in the liquid surface
Surface tension
• Surface tension tend to reduce the surface
area of a body of liquid
• The internal pressure within the droplet, p
and the surface tension forces, must be in
equilibrium.
 
p

37. Surface tension
• Taking vertical equilibrium of the forces acting on
the droplet
• The magnitude of surface tension forces are very
small compared to other forces
• Normally are neglected
2
2 r
p
r 

 
r
p

2

2
pr

 Units : N/m

38. 5. VAPOR PRESSURE, Pv
Vapor pressure
• defined as the pressure at which a liquid
turns to vapour
• the pressure exerted by its vapor in phase
equilibrium with its liquid at a given temperature
• The molecules which moves above the surface of
the liquid exert pressure in the confined surface
Vapor pressure
Pvapour = P saturation
Units: N/m2 or Pascal

39. 6. CAPILLARITY
When a liquid comes into contact with a solid surface:
- Adhesion forces: forces between solid and liquid
- Cohesion forces: forces within liquid
If cohesive forces > adhesive forces, the meniscus in a glass tube will take
a shape as in figure (a) and (b).
Figure (a) and (b)

40. Capillary effect is
the rise or fall of a
liquid in a small-
diameter tube
gd
h


 cos
4

gr
h


 cos
2

d
h


 cos
4

@ @
Units= m @ mm
where h = height of capillary rise (or depression)
 = surface tension
 = wetting (contact) angle
 = specific weight of liquid
r = radius of tube