Basic Concepts and Definitions Distinction between a fluid and a solid

1
Lecture
On
Fluid Mechanics
Er. Dharmendra Kushwaha [B.Tech., M.Tech.,& Ph.D.(P)]
Assistant Professor, Civil Engineering Department
Faculty of Engineering of Technology
Swami Vivekanand Subharti University, Meerut

2
Table of Contents
Basic Concepts and Definitions
Distinction between a fluid and a solid
Properties of Fluids
Viscosity-Kinematic and dynamic viscosity
Variation of viscosity with temperature
Newton law of viscosity
Type of Fluid
Surface Tension and Capillarity
References

3
Definition of a Fluid
A substance
that can flow
and take the
shape of its
container.
Includes
liquids and
gases.

4
Basic Concepts and Definitions
Fluid Mechanics is that branch of Engineering -Science which deals with the behaviour of
the 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 and if the pressure forces are also considered for the fluid in motion, that
branch of science is called fluid dynamics

5
Distinction Between Fluids and Solids
Solids
Have a definite
shape and
volume
Maintain their
shape unless a
force is applied
Fluids (Liquid & Gas)
Do not have a
definite shape.
Take the shape
of their container

6
PROPERTIES OF FLUID
1.Density or Mass Density
The density of a fluid is defined as
the ratio of the mass of a fluid to its
volume.
ρ =
Where:
ρ– density (kg/)
m – mass (kg)
V –Volume()
The value of density of Water is 1gm/
or 1000 kg/ .
2.Specific Weight or Weight
Density
The ratio between the weight of a fluid to
its volume.
Thus, ω =
=
ω = ρg N/
The value of specific weight for water is
9.81x 1000 N/ in SI units.

7
3.Specific Volume
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 is called
specific volume.
Mathematically, it is expressed as-
Specific Volume =
4.Specific Gravity
Specific gravity is defined as the ratio of the weight
density (or density) of a fluid to the weight density
(or density) of a standard fluid.
For liquids, the standard fluid is taken water and for
gases, the standard fluid is taken air. Specific gravity
is also called relative density. It is dimensionless
quantity and is denoted by the symbol S.
S(for Liquids) =
S(for Gases) =
Thus, weight density of a liquid
= S x Weight density of water
= S x 1000 x 9.81 N/m3
Thus, density of a liquid = S x Density of water
= S x 1000 kg/ m3
Mass of 𝑓𝑙𝑢𝑖𝑑
Volume of Fluid
= 1
ρ
=
 Thus specific volume is the reciprocal of mass
density. It is expressed as m3/kg.
 It is commonly applied to gases.
1

8
Example1.1: Calculate the specific weight, density and specific gravity of
one liter of a liquid which weighs 7 N.

9
Example 1.2: Calculate the density, specific weight and weight of one liter of
petrol of specific gravity = 0.7

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Viscosity
It is defined as the property of a fluid which
offers resistance to the movement of one
layer of fluid over another 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 as shown in Fig.
1.1, the viscosity together with relative
velocity causes a shear stress acting between
the fluid layers.
This shear stress is proportional to the rate of
change of velocity with respect to y. It is
denoted by symbol τ called Tau.
Source: R.K. Bansal
Figure 1.1: Velocity variation near
a solid boundary

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represents the rate of shear strain or rate of shear deformation or velocity gradient and µ is known as
constant of proportionality and known as coefficient of dynamic viscosity or only viscosity.
From equation (1.2) we have
τ
The unit of viscosity is obtained by putting the dimension of the quantities in equation 1.3
Mathematically, or τ = µ
(1.3)
µ =
Unit of Viscosity

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SI Unit of Viscosity = =
It is defined as the ratio between the dynamic viscosity and density of fluid. lt is denoted by the
Greek symbol (ν) called 'nu' . Thus, mathematically,
Kinematic Viscosity (ν) = =
The SI unit of kinematic viscosity is m2/s and in CGS unit it is written as cm2/s and known as stoke.
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, it is expressed as given by equation 1.2
Kinematic Viscosity
Newton's Law of Viscosity

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Fluids which obey the above relation are known as Newtonian fluids and the fluids which do not obey
the above relation are called Non-Newtonian fluids.
Variation of Viscosity with Temperature
 The viscosity of liquids decreases with the increase of temperature while the viscosity of gases
increases with increase of temperature. This is due to reason that the viscous forces in a fluid are
due to cohesive forces and molecular momentum transfer.
 In liquids, the cohesive forces predominates the molecular momentum transfer due to closely
packed molecules and with the increase in temperature, the cohesive forces decreases with the
result of decreasing viscosity.
 But in the case of gases the cohesive force are small and molecular momentum transfer
predominates. With the increase in temperature, molecular momentum transfer increases
and hence viscosity increases.

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The relation between viscosity and temperature for liquids and gases are:

15
Types of Fluid
1. Ideal Fluid: A fluid, which is incompressible and is having no viscosity, is
known as an ideal fluid. Ideal fluid is only an imaginary fluid as all the fluids,
which exist, have some viscosity.
2. Real fluid: A fluid, which possesses viscosity, is known as real fluid. All the
fluids in actual practice, are real fluids.
3. Newtonian Fluid: A real fluid, in which the shear stress is directly
proportional to the rate of shear strain (or velocity gradient), is known as a
Newtonian fluid.
4. Non-Newtonian fluid: A real fluid, in which shear stress is not proportional
to the rate of shear strain (or velocity gradient), known as a Non-Newtonian
fluid.
5. 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 (or velocity
gradient), is known as ideal plastic fluid.
Source: R.K. Bansal

16
Example 1. 3: If the velocity distribution over a plate is given by u = 2/3 y - in which u is velocity in
metre per second at a distance y metre above the plate, determine the shear stress at y = 0 and y=
0.15 m. Take dynamic viscosity of fluid as 8.63 poises.

18
Surface Tension and Capillarity
 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 behave like a membrane under tension.
 The magnitude of this force per unit length of the free
surface will have the same value as the surface energy per
unit area.
 Surface tension is created due to the unbalanced cohesive
forces acting on the liquid molecules at the fluid surface.
 It is denoted by Greek letter σ (sigma). In SI unit is denoted
by N/m.

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Capillarity
 It is defined as a phenomenon of rise or fall of a fluid
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 liquid surface is also known as capillary rise
while the fall of the liquid surface is known as capillary
depression.
 It is expressed in the terms of cm or mm of liquid. Its
value is depends upon the specific weight of the liquid,
diameter of the tube and surface tension of the liquid.

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Expression for Capillary Rise and Fall
The rise of water in capillary h =
The fall of water in capillary h =
Where, = Surface Tension
= Angle of contact between liquid and glass tube
The value of for water and glass tube = 0
The value of for mercury and glass tube = 90°

Reference
• A Textbook of Fluid Mechanics and Hydraulic Machines R. K. Bansal reprint, revised Publisher Laxmi
Publications, 2004 ISBN 8131808157, 9788131808153.
• https://www.google.com
• Introduction to Fluid Mechanics by Addisu D. March, 2013
• https://www.slideshare.net/login?from_source=%2F
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