Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics – concept of control volume - application of continuity equation, energy equation and momentum equation.

1. FLUID MECHANICS
 Fluid mechanics is that branch of science which deals
with the behavior of fluids (liquids or gases) at rest as
well as in motion.
 This branch of science deals with the static,
kinematics and dynamic aspects of fluids.
 The study of fluids at rest is called fluid statics.
 The study of fluids in motion, where pressure forces
are not considered, is called fluid kinematics.
 The pressure forces are also considered for the fluids
in motion, that branch of science is called fluid
dynamics.

2. UNIT-I
FLUID PROPERTIES AND FLOW
CHARACTERISTICS

3. SYLLABUS
Units and dimensions- Properties of fluids- mass
density, specific weight, specific volume, specific
gravity, viscosity, compressibility, vapor pressure,
surface tension and capillarity. Flow
characteristics– concept of control volume -
application of continuity equation, energy
equation and momentum equation.

4. DEFINE FLUID
 A fluid (or) liquid, which is capable of flowing.
It has no own shape, but confirms to the shape of
the containing vessels.
A fluid is a substance that
continually deforms under an applied shear stress
Liquids are like water, milk, air, steam.
MATTER EXISTS IN TWO STATES:
solids and the fluids.
fluids state being commonly divided into the
liquid and gaseous states.

5. DIFFERENCES BETWEEN SOLIDS
AND FLUIDS
 A solid is generally own shape and change in volume
under pure compressive load.
 It resistance to change in shape without a change in
volume under the application of tangential forces.
 The spacing and latitude of motion of molecules are
very small in solids, large in a liquid and extremely
large in gas.
 The intermolecular bonds are very strong in solids,
weak in liquids and very weak in gases.
 Solids are very compact and rigid. Solids materials
are steel, wood, plastics etc.

8. UNITS AND DIMENSIONS
 The word dimensions are used to describe basic concepts like mass,
length, time, temperature and force. Units are the means of expressing
the value of the dimension quantitatively or numerically.
 All physical quantities are measured by units.
There are two types of units:
(i). Fundamental units.
(ii). Derived units.
FUNDAMENTAL UNITS.
All physical quantities are expressed the following :
1.Length(L)
2.Mass(M)
3.Time(T)
DERIVED UNITS.
 Derived units are expressed in terms of fundamental units, this are area,
velocity, pressure etc.

9. SYSTEM OF UNITS
CGS Units
 The fundamental units of length, mass and time are taken as
centimeter, gram and second respectively.
FPS Units
 The fundamental units of length, mass and time are taken as
feet, pound and second respectively.
MKS Units
 In this system, the fundamental units of length, mass and time
are taken as meter, kilogram, and seconds respectively.
 The MKS units are called as gravitational units or engineers
units.
SI Units
 This system has six basic units, two supplementary units and
twenty seven derived units.

10. S.I Six Basic Units
Quantity SI Unit Dimension
Length Metre, m L
Mass Kilogram, kg M
Time Second, s T
Temperature Kelvin, K
Current Ampere, A I
Luminosity Candela Cd

11. Two Supplementary Units
One is for measuring the plane angle called
radian(rad).
Another for measuring solid angle called
stearadian(Sr).

12. Derived Units
Quantity SI Unit
Volume m3
Area m2
velocity m/s
Discharge m3 /s
acceleration m/s2
force N
Torque, energy,
work
Joule J (or) N m
power Watt W
pressure ( or stress) N/m2
density kg /m3
Dynamic viscosity N s/m2
surface tension N/m
Kinematic viscosity m2/s

13. Thermal conductivity W/mK
Specific heat J/kgK
Entropy J/K
Momentum Kg-m/s
Weight density N/m3
Frequency Hz
Angular velocity Rad/s
Angular acceleration Rad/s2

14. DIFFERENT TYPES OF FLUIDS
Basically the fluids are classified into 5 types
and these are
1. Ideal fluid
2. Real fluid
3. Newtonian fluid
4. Non-Newtonian fluid, and
5. Ideal plastic fluid

16. Ideal Fluid
 A fluid which is incompressed and have no viscosity falls in the category of ideal
fluid.
 Ideal fluid is not found in actual practice but it is an imaginary fluid because all
the fluid that exist in the environment have some viscosity. there in no ideal fluid in
reality.
Real Fluid
 A fluid which has at least some viscosity is called real fluid.
 Actually all the fluids existing or present in the environment are called real fluids..
Newtonian Fluid
 If a real fluid obeys the Newton's law of viscosity (i.e the shear stress is directly
proportional to the shear strain) then it is known as the Newtonian fluid.
 Example: water, kerosene
Non-Newtonian Fluid
 If real fluid does not obeys the Newton's law of viscosity then it is called Non-
Newtonian fluid.
 Example: paint, toothpaste
Ideal Plastic Fluid
 A fluid having the value of shear stress more than the yield value and shear stress
is proportional to the shear strain (velocity gradient) is known as ideal plastic fluid.

17. PROPERTIES OF FLUIDS
Density (or) Mass Density:(ρ)
 Density or mass density of a fluid is defined as the ratio
of the mass of a fluid to its volume.
 Thus mass per unit volume of a fluid is called density.
 ρ = Mass of fluid / Volume of fluid
 Its units ,kg/m3
 Temperature increase with density decrease
 Pressure increase with density increase
 To estimate the density from characteristic gas equation
of Pv = mRT (R= 287J/kgK (or) 0.287 KJ/kg)
 Water = 1000 kg/m3, Mercury = 13600 kg/m3, Air = 1.23
kg/m3, Paraffin Oil = 800 kg/m3.
 (at pressure =1.013 N/m2, and Temperature = 288.15 K.)

18. Specific weight or weight density:(w)
 Specific weight or weight density of a fluid is the ratio
between the weight of a fluid to its volume.
 The weight per unit volume of a fluid is called Specific
weight or weight density
 It various from place to place because of acceleration due
to gravity changing from place to place.
 Specific weight, w = Weight of fluid / Volume of fluid
 w = ρg (w=W/V = mg/V = ρg)
 Its units, N/m3
 Temperature increase with specific weight decrease
 Pressure increase with specific weight increase
 Water =9810 N/m3, Mercury = 132943 N/m3, Air =12.07
N/m3, Paraffin Oil =7851 N/m3

19. Specific Volume:(v)
Specific volume of a fluid is defined as the
volume of a fluid occupied by a unit mass or
volume per unit mass of a fluid.
 v = Volume of fluid / Mass of fluid
= 1/ ρ
Its units, m3/kg

20. Specific Gravity (or) Relative Density :(S)
 Specific gravity is defined as the ratio of the density
of a fluid to density of a standard fluid.
 S = density of a fluid / density of a standard fluid.
 Specific gravity of mercury is 13.6

21. Viscosity
 Viscosity is the property of a fluid, due to cohesion and interaction between
molecules, which offers resistance to sheer deformation.
 Different fluids deform at different rates under the same shear stress.
 Fluid with a high viscosity such as syrup, deforms more slowly than fluid with a
low viscosity such as water.
 Shear stress,

22. Viscosity is defined as the property of a fluid which offers resistance to the
movement of one layer of fluid over adjacent layer of the fluid.
When two layers of a fluid, a distance ‘dy’ apart, move one over the other at different
velocities, say u and u+du.
The viscosity together with relative velocity causes a shear stress acting between the
fluid layers.
The top layer causes a shear stress on the adjacent lower layer while the lower layer
causes a shear stress on the adjacent top layer.
This shear stress is proportional to the rate of change of velocity with respect to y.

23. Dynamic Viscosity (µ):
 Its defined as the Shear stress(τ), required causing
unit rate of shear deformation(du/dy).
 µ = τ /(du/dy).
 Its units, N-s/m2 (or) kg/m-s (or) poise
Kinematic Viscosity (ν):
 Its defined as the ratio of dynamic viscosity to mass
density.
 Its units, m2/s (or) stoke

24. VAPOUR PRESSURE
H2O(g)
molecules
(water vapor)
H2O(l)
molecules

25. VAPORIZATION:
• A change from the liquid state to the gaseous state is known as
vaporization.
VAPOUR PRESSURE:
• The liquid is kept in closed vessel.
• The vaporization take place, the molecules escapes from the free
surface of the liquid.
• This vapour molecules occupies the space b/w free liquid surface
and the top of the vessel.
• These accumulated vapours exert a pressure on the liquid surface.
• This pressure is called the vapour pressure of the liquid.
• Water vapour pressure is 2337N/m2 at 200C, but 101325N/m2 at
1000C.

26. SURFACE TENSION
 Surface tension is defined as the tensile force acting on the surface of a
liquid in contact with a gas or on the surface between two immiscible
liquids such that the contact surface behaves like a membrane under
tension.
 Due to molecules attraction, liquids have properties of cohesion and
adhesion.
 Cohesion is due to the force of attraction b/w molecular of same liquid.
 This force is very small.
 Adhesion is due to the force of attraction b/w the molecules of two
different liquid.
 The molecules of the liquid and molecules of solid surface

28. BULK MODULUS
 It define as the ratio of change in pressure to the rate of
change of volume is called as bulk modulus of the material.
 Bulk modulus (K) = (change in pressure) /
(volumetric strain)
 K = -(dp/(dV/V))
 Volumetric strain is the change in volume divided by the
original volume. (dV/V)
 Negative sign for dV indicates the volume decreases as
pressure increases.
 K = dp/(dρ/ρ) [dV/V = - dρ/ρ]
 Typical values of Bulk Modulus:
• K = 2.05 x 109 N/m2 for water
• K = 1.62 x 109 N/m2 for oil.

29. COMPRESSIBILITY
 The compressibility of a fluid is the reduction of the volume of the
fluid due to an external pressure acting on it.
 A compressible fluid will reduce (or) change in volume in the
presence of external pressure.
 Compressibility is the reciprocal of the bulk modulus of elasticity, K
which is defined as the ratio of compressive stress to volumetric
strain.
 Compressibility is given by = 1/K
 Its unit in N/m2
 In nature all the fluids are compressible. Gases are highly
compressible but liquid s are not highly compressible.
Relationship b/w bulk modulus (K) and Pressure(P) for a gas
 The relationship b/w bulk modulus of elasticity(K) and Pressure for
a gas for two different processes of compression are as:
(i). Isothermal process.
(ii). Isentropic (or) adiabatic process.

30. CAPILLARITY
 Capillarity is defined as a phenomenon of rise or fall of a
liquid surface relative to the adjacent general level of liquid in
a small tube, when the tube is held vertically in the liquid
 Capillarity occurs because of intermolecular forces b/w the
liquid and surrounding solid surface. And due to pressure of
cohesion and adhesion which cause the liquid work against
gravity
 It is expressed in terms of cm or mm of liquid.
 Its value depends upon the specific weight of the liquid,
diameter of the tube and surface tension of the liquid.

31. CAPILLARY RISE
 If the glass tube is inserted vertically in a liquid, say water. The liquid
will rise in the tube above the level of the liquid surface is known as
capillary rise
 σ = Surface tension of liquid.
 θ = Angle of contact b/w liquid and glass tube.
 The Weight of liquid of height h in the tube = (Area of tube x h) x ρ x g
= (π/4 x d2 x h) x ρ x g ------------------------- (i)
 Vertical component of the surface tensile force = (σ x Circumference) x cos θ
= σ x πd x cos θ ------------------------------- (ii)
Equating equation (i) & (ii)
 (π/4 x d2 x h) x ρ x g = σ x πd x cos θ
 h = σ x πd x cos θ / (π/4 x d2) x ρ x g
 h = 4 σ cos θ / ρ x g x d

32. CAPILLARY DEPRESSION
 If the glass tube is dipped vertically in a liquid, say mercury. The level of
mercury in the tube will be lower than the general level of the outside
liquid.
 Two forces are acting on the mercury inside the tube.
 First one is due to surface tension acting in the down ward direction
and equal to σ x πd x cos θ --------- (i)
 Second force is due to hydrostatic force acting upward and is equal to
intensity of pressure at a depth ‘h’ x Area
= p x (π/4 x d2 ) = ρg x h x (π/4 x d2 ) -------------- (ii)
• Equating equation (i) & (ii)
• σ x πd x cos θ = ρ x g x h x (π/4 x d2 )
• h = 4 σ cos θ / ρ x g x d

33. APPLICATION OF BERNOULLI’S
EQUATION
• Venturi meter
• Orifice meter
• Pitot tube

34. VENTURIMETER

36. VENTURI METER

39. ORIFICE METER

41. ORIFICE METER

43. PITOT TUBE