1. UNIT 1 INTRODUCTION
CE6451 FLUID MECHANICS &
MACHINERY
BY
Dr. A. Asha
Professor/Mechanical Engineering
Kamaraj College of Engineering & Technology, Virudhunagar
2. INTRODUCTION TO FLUID MECHANICS
โข Fluid mechanics is the branch of science which deals with the
behaviour of fluids at rest and in motion
โข Fluid mechanics is classified as
Fluid statics
Fluid dynamics is classified as
a. Fluid kinematics
b. Fluid kinetics
3. PROPERTIES OF FLUIDS
โข Density or Mass density (ฯ) : It is defined as the ration of the mass of the fluid
to the volume of the fluid
๐ =
๐๐๐ ๐ ๐๐ ๐๐๐ข๐๐
๐ฃ๐๐๐ข๐๐ ๐๐ ๐๐๐ข๐๐
๐ of water = 1000 kgm /m3
units : kgm /m3
โข Specific weight or weight density (w) : It is defined as the weight of the fluid
volume of the fluid
w=
๐ค๐๐๐โ๐ก ๐๐ ๐กโ๐ ๐๐๐ข๐๐
๐ฃ๐๐๐ข๐๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐
=
๐๐๐ ๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐ ร๐๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐
๐ฃ๐๐๐ข๐๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐
w = ๐ รg
units : N/m3 w of water = 9810 N/m3
4. PROPERTIES OF FLUIDS
โข Specific volume : It is defined as the reciprocal of density of the fluid
specific volume =
๐ฃ๐๐๐ข๐๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐
๐๐๐ ๐ ๐๐ ๐กโ๐ ๐๐๐ข๐๐
Units : m3/ kgm
โข Specific gravity (S): It is defined as the ratio of the density of the liquid
to the density of water (OR) it is defined as the ratio of the weight
density of the liquid to the weight density of water.
S =
๐ ๐๐ ๐๐๐๐ข๐๐
๐ ๐๐ ๐ค๐๐ก๐๐
(OR)
๐ค ๐๐ ๐๐๐๐ข๐๐
๐ค ๐๐ ๐ค๐๐ก๐๐
5. PROPERTIES OF FLUIDS
โข Viscosity : It is defined as the property of the fluid which offers resistance to the
movement of one layer of the fluid over another adjacent layer of the fluid.
โข Newtons law of viscosity (ยต) : It states that the shear stress (ฯ) on a fluid element
layer is directly proportional to the rate of shear strain. The constant of
proportionality is called the co-efficient of viscosity. Mathematically
ฯ = ๐
๐๐ข
๐๐ฆ
Units of dynamic viscosity = Ns/m2 , poise
1 poise = 0.1 Ns/m2
โข Kinematic viscosity (ฯ)
ฯ=
๐
๐
It is defined as the ratio of dynamic viscosity of the
fluid to the density of the fluid.
Units of kinematic viscosity = m2 /s , stokes
I stoke = 1 cm2/s
6. PROPERTIES OF FLUIDS
โข Compressibility and Bulk modulus :
Compressibility is defined as the reciprocal of bulk modulus.
Bulk modulus (K) is defined as the ratio of compressive stress to volumetric strain
K =
๐ฐ๐๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐
โ๐ ๐/๐
Surface Tension (ฯ) = Surface tension is defined as the force acting on the surface
of a liquid in contact with a gas or on the surface between two immiscible fluids
such that the contact surface behaves like a membrane under tension.
Units : N/m
For liquid droplet h=
๐๐
๐
For soap bubble h=
๐๐
๐
Capillarity : It is defined as the phenomenon of rise or fall of a liquid surface in a
small tube relative to the adjacent general level of liquid when the tube is held
vertically in the liquid. The rise of the liquid surface is capillary rise while the fall in
the liquid surface is known as capillary depression
For capillary rise h=
๐๐
๐๐๐
For capillary depression
h=
๐๐๐๐๐๐ฝ
๐๐๐
Where ฮธ = angle of contact between liquid and glass tube.
7. TYPES OF FLUIDS
โข Ideal fluid : A fluid which is incompressible and is having no viscosity
is known as ideal fluid. Ideal fluid is an imaginary fluid
โข Real fluid : A fluid which possess viscosity is known as real fluid. All
fluids in practice are known as real fluid
โข Newtonian fluids : a real fluid in which the shear stress is directly
proportional to the rate of shear strain is called as Newtonian fluid
โข Non โ Newtonian fluid : a real fluid in which the shear stress is not
proportional to the rate of shear strain is known as non Newtonian
fluid
โข Ideal plastic fluid : A fluid in which shear stress is more than the yield
value and shear stress is proportional to the rate of shear strain is
known as ideal plastic fluid
8. TYPES OF FLOW
โข Steady flow : a steady flow is a flow in which the fluid characteristics
like pressure, density, etc does not vary with respect to time
โข Un steady flow : a unsteady flow is a flow in which the fluid
characteristics like pressure, density, etc vary with respect to time
โข Uniform flow : A flow in which the velocity at any given time does not
change with respect to distance
โข Non uniform flow : A flow in which the velocity at any given time
change with respect to distance
โข Compressible flow : The flow in which the density of the fluid changes
from point to point ฯโ ๐๐๐๐ ๐ก๐๐๐ก,
โข Incompressible flow : The flow in which the density of the fluid do not
change from point to point ฯ = ๐๐๐๐ ๐ก๐๐๐ก
9. RATE OF FLOW (OR) DISCHARGE
โข It is defined as the quantity of a fluid flowing per second through a
section of a pipe or a channel. For an incompressible fluid the rate of
flow or discharge is expressed as the volume of the fluid flowing
across the section per second.
โข For incompressible fluids (Q) = A ร V
Where A = Cross sectional area of the pipe
V = average velocity of fluid across the section
10. CONTINUITY EQUATION
โข The equation is based on the law of conservation of mass
โข It states that for a fluid flowing through the pipe at all the cross section the quantity of the fluid
per second is a constant.
โข Consider two cross sections of a pipe as shown in the fig
Let V1 be the velocity at cross section 1-1 Let V2 be the velocity at cross section 2-2
Let A1 be the velocity at cross section 1-1 Let A2 be the velocity at cross section 2-2
According to the law of conservation of mass
Rate of flow at section 1-1 = Rate of flow at section 2-2
๐ ๐ ๐จ ๐ ๐ฝ ๐ = ๐ ๐ ๐จ ๐ ๐ฝ ๐
this is the general expression for both compressible and incompressible fluids
For incompressible fluid the above equation is ๐จ ๐ ๐ฝ ๐ = ๐จ ๐ ๐ฝ ๐ because density is constant
1
1
2
2
11. BERNOULLIS THEOREM
โข It states that in a steady, ideal flow of an incompressible fluid the total energy at any
point of the fluid is constant. The total energy consists of pressure energy, kinetic
energy and datum energy. Thus mathematically bernoullis equation is written as
๐
๐๐
+
๐ ๐
๐๐
+ ๐ = ๐ช๐๐๐๐๐๐๐
๐
๐๐
= Pressure energy
๐ ๐
๐๐
= Kinetic energy
Z = datum energy
โข Assumptions of Bernoulli's equation :
1. The fluid is ideal
2. The flow is steady
3. The flow is incompressible
4. The flow is irrotational
13. APPLICATIONS OF BERNOULLIS EQUATION
โข Venturimeter
โข Orificemeter
โข Pitot tube
Venturimeter :
The venturimeter is a device which is used to measure the rate of flow through a closed pipe
It consists of 3 parts
(a) A short converging part
(b) Throat
(c) Diverging part
Theoretical discharge
Cd =
๐ธ ๐๐๐๐๐๐
๐ธ ๐ป๐๐๐๐๐๐๐๐๐๐
a1 = area of the pipe a2 = area of the throat
h= x
๐ ๐
๐ ๐
โ ๐ ๐ ๐ = specific gravity of manometric fluid for mercury = 13.6
๐ ๐ = ๐ฌ๐ฉ๐๐๐ข๐๐ข๐ ๐ ๐ซ๐๐ฏ๐ข๐ญ๐ฒ ๐จ๐ ๐ฐ๐๐ญ๐๐ซ for water = 1
14. ORIFICEMETER
โข It is a device used for measuring the rate of flow of a fluid through a
pipe. It consists of a flat circular plate which has a circular sharp
edged hole called as orifice which is concentric to the pipe
15. DISCHARGE OF ORIFICEMETER
โข Let a1 = area of the pipe a0 = area of the orifice
โข Actual discharge
h= x
๐ ๐
๐ ๐
โ ๐
๐ ๐ = specific gravity of manometric fluid for mercury = 13.6
๐ ๐ = ๐ฌ๐ฉ๐๐๐ข๐๐ข๐ ๐ ๐ซ๐๐ฏ๐ข๐ญ๐ฒ ๐จ๐ ๐ฐ๐๐ญ๐๐ซ for water = 1