UNIT 1 INTRODUCTION
CE6451 FLUID MECHANICS &
MACHINERY
BY
Dr. A. Asha
Professor/Mechanical Engineering
Kamaraj College of Engineering & Technology, Virudhunagar
INTRODUCTION TO FLUID MECHANICS
• Fluid mechanics is the branch of science which deals with the
behaviour of fluids at rest and in motion
• Fluid mechanics is classified as
Fluid statics
Fluid dynamics is classified as
a. Fluid kinematics
b. Fluid kinetics
PROPERTIES OF FLUIDS
• Density or Mass density (ρ) : It is defined as the ration of the mass of the fluid
to the volume of the fluid
𝜌=
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
𝜌 of water = 1000 kgm /m3
units : kgm /m3
• Specific weight or weight density (w) : It is defined as the weight of the fluid
volume of the fluid
w=
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
w = 𝜌 ×g
units : N/m3
=
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 ×𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
w of water = 9810 N/m3
PROPERTIES OF FLUIDS
• Specific volume : It is defined as the reciprocal of density of the fluid
specific volume =
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
Units : m3/ kgm
• 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=
𝜌 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑
𝜌 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
(OR)
𝑤 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑
𝑤 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
PROPERTIES OF FLUIDS
• 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.
• Newtons law of viscosity (µ) : It states that the shear stress (τ) 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
τ=𝜇
𝑑𝑢
𝑑𝑦
Units of dynamic viscosity = Ns/m2 , poise
1 poise = 0.1 Ns/m2
• Kinematic viscosity (ϒ)
𝜇
ϒ= It is defined as the ratio of dynamic viscosity of the
𝜌
fluid to the density of the fluid.
Units of kinematic viscosity = m2 /s , stokes
I stoke = 1 cm2/s
PROPERTIES OF FLUIDS
• 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
𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒇 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆
K=
−𝒅𝒗/𝒗
Surface Tension (σ) = 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
𝟒𝝈
𝟖𝝈
For liquid droplet h=
For soap bubble h=
𝒅
𝒅
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
𝟒𝝈
For capillary rise
h=
For
capillary
depression
𝝆𝒈𝒅
𝟒𝝈𝒄𝒐𝒔𝜽
h=
𝝆𝒈𝒅
Where θ = angle of contact between liquid and glass tube.
TYPES OF FLUIDS
• Ideal fluid : A fluid which is incompressible and is having no viscosity
is known as ideal fluid. Ideal fluid is an imaginary fluid
• Real fluid : A fluid which possess viscosity is known as real fluid. All
fluids in practice are known as real fluid
• Newtonian fluids : a real fluid in which the shear stress is directly
proportional to the rate of shear strain is called as Newtonian fluid
• Non – 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
• 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
TYPES OF FLOW
• Steady flow : a steady flow is a flow in which the fluid characteristics
like pressure, density, etc does not vary with respect to time
• Un steady flow : a unsteady flow is a flow in which the fluid
characteristics like pressure, density, etc vary with respect to time
• Uniform flow : A flow in which the velocity at any given time does not
change with respect to distance
• Non uniform flow : A flow in which the velocity at any given time
change with respect to distance
• Compressible flow : The flow in which the density of the fluid changes
from point to point ρ≠ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡,
• Incompressible flow : The flow in which the density of the fluid do not
change from point to point ρ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
RATE OF FLOW (OR) DISCHARGE
• 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.
• For incompressible fluids (Q) = A × V
Where A = Cross sectional area of the pipe
V = average velocity of fluid across the section
CONTINUITY EQUATION
• The equation is based on the law of conservation of mass
• 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.
• Consider two cross sections of a pipe as shown in the fig
1
2
2
1
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
𝝆𝟏 𝑨𝟏 𝑽𝟏
= 𝝆𝟐 𝑨𝟐 𝑽𝟐
this is the general expression for both compressible and incompressible fluids
For incompressible fluid the above equation is 𝑨𝟏 𝑽𝟏 = 𝑨𝟐 𝑽𝟐 because density is constant
BERNOULLIS THEOREM
• 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
𝒑
𝝆𝒈
𝒗𝟐
+
𝟐𝒈
+ 𝒛 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝒑
𝝆𝒈
= Pressure energy
𝒗𝟐
𝟐𝒈
= Kinetic energy
Z = datum energy
• 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
DERIVATION OF EULERS AND BERNOULLIS
EQUATION
APPLICATIONS OF BERNOULLIS EQUATION
• Venturimeter
• Orificemeter
• 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 = 𝑸
𝑸𝒂𝒄𝒕𝒖𝒂𝒍
𝑻𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍
a1 = area of the pipe a2 = area of the throat
h= x
𝒔𝒎
𝒔𝒇
−𝟏
𝒔𝒎 = specific gravity of manometric fluid
𝒔𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫
for mercury = 13.6
for water
=1
ORIFICEMETER
• 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
DISCHARGE OF ORIFICEMETER
• Let a1 = area of the pipe a0 = area of the orifice
• Actual discharge
h= x
𝒔𝒎
𝒔𝒇
−𝟏
𝒔𝒎 = specific gravity of manometric fluid
𝒔𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫
for mercury = 13.6
for water
=1
PITOT TUBE
PITOT TUBE
MOMENTUM EQUATION