11. COURSE OUTCOMES
C303.1. Understand the basic properties of fluids like mass density,
specific weight, specific gravity, specific volume, viscosity,
cohesion, adhesion, surface tension, capillarity, vapour pressure of
liquid, compressibility and bulk modulus, pressure inside a water
droplet, pressure inside a soap bubble and liquid jet and apply
Newton's law of viscosity in solving practical problems related to
19. COURSE OUTCOMES
C303.3.Understand the significance of basic principles of fluid
statics and application of hydrostatic law in determining forces on
horizontal, vertical and inclined and curved surfaces and hydraulic
structures like dam and lock gates
21. COURSE OUTCOMES
C303.4.Understand the principles of kinematics with specific
emphasis on application of three-dimensional continuity equation in
Cartesian coordinate system, stream function, velocity potential,
orthogonality of streamlines and equipotential lines for rotational
and irrotational motion of fluid
27. COURSE OUTCOMES
C303.5. Apply the principles of Bernoulli's equation in
measurement of discharge through horizontal Venturimeter, orifice
meter, pitot tube and apply momentum equation in pipe bend and
also to determine discharge through notches and weirs such as
rectangular, triangular, trapezoidal, Cippoletti, broad crested and
32. COURSE OUTCOMES
C303.6. Apply fundamental concepts of fluid mechanics in solving
fluid flow problems in pipes connected in parallel and series, head
losses in pipe due to friction and sudden expansion, design of pipe
and analysis of pipe networks by Hardy cross method and also to
study the effect of water hammer due to sudden and gradual closure
of rigid and elastic valve.
Write the suitable physical units for the following quantities:
1. Length =--------------
2. Mass =----------------
3. Time =----------------
4. Area =----------------
7. Angular velocity=---------------
9. Angular acceleration=-----------------
11. Acceleration due to gravity=---------------
12. Kinematic viscosity=-----------------
35. MODULE 1
FLUIDS AND ITS PROPERTIES
Fluids mechanics is that branch of science which deals with the behavior of
fluids ( liquids or gases) at rest as well as in motion.
Thus this branch of science deals with statics, kinematics and dynamic aspects
The study of fluids at rest is called as fluids statics
The study of fluids at motion, where pressure forces are not considered, then
the study is called as fluids kinematics.
The study of fluids at motion, where pressure forces are considered , then the
study is called as fluids dynamics.
36. PROPERTIES OF FLUIDS
Density or Mass density:
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 mass density.
It is denoted by the symbol “ρ” (rho).
The unit of mass density in SI unit is kg per cubic meter (kg/m3)
The value of density of water is 1000 kg per cubic meter.
Specific weight or weight density:
Specific weight or weight density of a fluid is the ratio between the weight of a
fluid to its volume. Thus weight per unit volume of a fluid is called weight
It is denoted by the symbol “w”.
The specific weight or weight density of water is 1000*9.81 N per cubic meter.
SI uni t of weight density is N/m3
37. Specific volume:
It 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.
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 gasses, standard fluid
is taken air.
Specific gravity is also called as relative density.
It is dimensionless quantity and is denoted by S.
Viscosity is defined as the property of a fluid which offers resistance to the
movement of one layer of fluid over another adjacent layer of a 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 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. It is
denoted by symbol τ (tau).
55. Surface Tension
Tensile force acting on a surface of a liquid in contact
with gas or on surface between two immiscible
liquids such that contact surface behaves like
membrane under tension.
It is denoted by σ (sigma).
Unit is N/m
56. All the molecules on free surface experience downward
Thus very thin film is formed at surface due to inward
molecular pull. (ie due to tension on free surface)
58. Surface tension on liquid droplet
Liquid droplets tend to assume a spherical shape
since a sphere has the smallest surface area per unit
The pressure inside a drop of fluid can be calculated
using a free-body diagram of a spherical shape which
is cut in to two halves of radius r.
Let σ = surface tension of the liquid
p= Pressure intensity inside the droplet
d= diameter of droplet
60. The force acting on one half will be
(i) Tensile force due to surface tension acting around
circumference of cut portion.
i.e.= σ x circumference
= σ x Πd
(ii) Pressure force on area
= p X (𝜋/4)𝑑2
At equilibrium, these two forces will be equal and opposite
p x (𝜋/4)𝑑2= σ x Πd
The above equation show that with increase in diameter of
droplet, pressure intensity decreases
Capillarity is a phenomenon of rise or fall of liquid
surface relative to the adjacent general level of liquid
when the tube is held vertically in liquid.
This phenomenon is due to the combined effect of
cohesion and adhesion of liquid particle.
The rise of liquid level is known as capillary rise whereas
the fall of liquid surface is known as capillary
depression.It is expressed in terms of cm or mm of liquid.
Armchair Animation Capillary Action.mp4
Capillary action is the ability of a liquid to flow in narrow
spaces without the assistan.mp4
66. The magnitude of capillarity is dependent upon
Diameter of tube.
Specific weight of liquid.
Surface tension of liquid.
67. Expression for Capillary rise
Consider a glass tube of
diameter ‘d’ opened at both
ends and is inserted in liquid.
The liquid will rise in tube
above the level of liquid.
Let h= Height of liquid in tube.
θ= the contact angle between
liquid and glass tube.
σ= surface tension of liquid.
At equilibrium, weight of
liquid on height ‘h’ is balanced
by force at the surface of liquid
in tube. This force is surface
68. The weight of the liquid column of height ‘h’ in the tube =
Area of the tube x h x Specific weight
The surface tension force acting around the circumference
of the tube = σ x πd.
The vertical component of this force = σ x πd x Cosθ —(i)
70. Expression for Capillary fall
The glass tube is dipped in mercury, the level of mercury
in tube will be lower than general level of outside liquid.
71. Bulk Modulus (K)
When a solid or fluid (liquid or gas) is subjected to a
uniform pressure all over the surface, such that the
shape remains the same, then there is a change in
Then the ratio of normal stress to the volumetric
strain within the elastic limits is called as Bulk
modulus. This is denoted by K.
72. where p = increase in pressure;
V = original volume;
ΔV = change in volume
The negative sign shows that with increase in
pressure p, the volume decreases by Δ V i.e. if p is
positive, Δ V is negative.
74. Vapour Pressure
Change of state from liquid to gaseous state is called
This occurs due to continuous escape of molecules
from free liquid surface.
Vaporization takes place at ……….temperature in
When vaporization takes place, molecules escapes
from free surface of the liquid and gets accumulated
in space between liquid surface and top of vessel.
These vapours exerted pressure on liquid surface.
This pressure is called vapour pressure of the liquid.
Mass, weight, density, weight density,
specific volume. (Formula and Units)
Viscosity- Dynamic and kinematic (Formula
and Units) Reason for viscosity?? Effect of
Cohesion, adhesion- Examples
Surface tension- (Formula and Units)
Capillarity- Capillary rise and fall (Formula
and Units) – Examples, day to day life
79. Fluid Pressure
Fluid is a state of matter which exhibits the property of
When a certain mass of fluids is held in static
equilibrium by confining it within solid boundaries
(Fig), it exerts force along direction perpendicular to
the boundary in contact. This force is called fluid
Pressure is one of the basic properties of all fluids.
Pressure (p) is the force (F) exerted on or by the fluid on a
unit of surface area (A).
The basic unit of pressure is Pascal (Pa). When a fluid
exerts a force of 1 N over an area of 1m2, the pressure
equals one Pascal, i.e., 1 Pa = 1 N/m2
1 bar =100kPa
1 Kpa=…….. N/m2
81. Pressure at a Point and Pascal’s Law
For a fluid at rest, the pressure at a given point is the
same in all directions.
States that “ pressure or intensity of pressure at a point in a
static fluid is equal in all directions
88. Absolute, gauge, atmospheric and vacuum
The pressure on fluid is measured in two different
In one system it is measured above complete vacuum
pressure or absolute zero pressure
Other system is measured above atmospheric
89. Absolute pressure:
It is defined as the pressure which is measured with
reference to absolute vacuum pressure.
It is defined as the pressure which is measured with
the help of pressure measuring instrument, in which
the atmospheric pressure is taken as datum. The
atmospheric pressure is marked as zero.
91. Vacuum pressure:
It is defined as the pressure below the atmospheric
Absolute pressure= Atmospheric pressure+ Gauge
Vacuum pressure= Atmospheric pressure- Absolute
92. Measurement of pressure
The pressure of a fluid is measure by the following
Manometers are defined as the devices used for
measuring the pressure at a point in a fluid by
balancing the column of fluid by the same or another
column of the fluid.
They are classified as
A) Simple manometers
B) Differential Manometers
94. SIMPLE MANOMETERS
A simple manometer consists of a glass tube having
one of its ends connected to a point where pressure is
to be measured and other end remains open to
Types of Simple Manometers are
Single column Manometer
It is the simplest form of manometer used for
measuring gauge pressures.
One end of this manometer is connected to the point
where the pressure is to be measured and the other
end is open to atmosphere.
The rise of liquid gives the pressure head at that
98. U- Tube Manometer
It consists of glass tube bent in U shape, one end of
which is connected to a point at which pressure is to
be measured and other end remains open to the
The tube generally contains mercury or any other
liquid whose specific gravity is greater than the
specific gravity of liquid whose pressure is to be
105. Mechanical pressure measuring devices
Mechanical Pressure Measurement Devices do not
read pressure of any system by deflection of liquid
level in some sort of tube.
Instead they use some solid object, such as, tube,
plate, or diaphragm to measure pressure.
The system whose pressure is to be measured is
connected to the deflecting object.
Any change in pressure causes the object to deflect
and this deflection is mechanically amplified, by
using a suitable gear and linkage mechanism, and
indicated on the calibrated dial.
107. Bourdon tube pressure gauge
Bourdon Gauge has a coiled tube whose one end is
connected to the system under consideration and
other end is sealed.
With the application of the pressure in the tube it
straightens up causing deflection of the sealed end.
The sealed end is connected to the indicating needle
through a gear and linkage mechanism.
The deflection of the sealed end results in movement
of the needle which moves on a calibrated dial.
Bourdon gauges can be used to measure a wide range
109. Diaphragm Gauge & Bellows Gauge
Diaphragm Gauge: Similar to the Bourdon Gauge,
but has a Diaphragm which deflects on pressure
changes and the deflection is indicated on the
Bellows Gauge: In such gauges indicating needle is
driven by the deflection of bellows chamber. This
gauge is suitable for measurement of very low
111. Electronic Pressure Transmitters /
Most electronic pressure sensors incorporate one of
the previously discussed elements are the primary
pressure detector, and it is used to vary a measurable
electrical quantity to produce a proportionately
variable electronic signal. Because the energy form is
transferred from a mechanical to an electrical
nature, these devices are often classified as
112. Strain Gauge
Strain is defined as a deformation or change in the shape of a
material as a consequence of applied forces. A strain gauge is a
device which uses the change of electrical resistance of a wire under
strain to measure pressure. The strain gauge changes a mechanical
motion into an electrical signal when a wire length is changed by
tension or compression, altering the wire diameter and, hence,
changing the electrical resistance. The change in resistance is a
measure of the pressure producing the mechanical distortion. This
is measured by a Wheatstone bridge circuit, preferably of the null
balance type, so that the strain gauge carries no current.
The complete measuring device includes a sensing element (
bourdon tube, bellows or diaphragm ), a strain gauge attached to
the element, a stable power source and a read out device. A strain
gauge element and a typical transducer is shown in the figure below