basic concepts of fluid mechanics (FM-1).pdf

FLUID MECHANICS-I
ME-204
Dr. Muhammad Uzair
Assistant Professor
Mechanical Engineering Department
NED University of Engineering & Technology
DICE Lab (MED, NED)
+99261261 (Ext. 2206)
uzair@neduet.edu.pk

Course Objectives
2
• To impart theoretical knowledge of fluid
statics and dynamics and to enable the
students to analyze and solve engineering
problems based on fluid mechanics.
• The course is designed to provide strong
foundation for the related subjects to be
taught in the latter part of Bachelor program.

Course Learning Outcomes
3
No. CLO PLO
Level of
Learning
1
To be able to define or describe different theoretical
terminologies and concepts used in fluid statics and
dynamics.
PLO-1 C1
2
To be able to apply pertinent equations of fluid
mechanics and solve different engineering
problems based on fluid statics and dynamics.
PLO-2 C2
3
To be able to analyze and solve dimensional
analysis problems.
PLO-2 C2
4
Observation, performance and analysis of
experimental work in fluid statics and dynamics
PLO-1 P1

Course Contents
4
Fluid Properties: Properties of fluids such as density, viscosity, compressibility, surface
tension and capillarity, types of fluids.
Fluid Statics: Pressure in a fluid at a point, variation of pressure with depth,
Homogeneous fluid, Several fluids of different specific weights, Interconnected vessels,
Rigid-body motion of fluid, Hydraulic circuits, Force on plane and curved surfaces,
Buoyancy and flotation, Stability of a floating body. Atmospheric equilibrium, Isothermal
state, Adiabatic state, The standard atmosphere.
Fluid Dynamics: System and control volume, classification of flows, velocity and
acceleration fields, stream lines, path lines, and streak lines, Equation of continuity,
Euler’s equations of motion, Bernoulli equation, Energy equation, Impulse and
momentum, One dimensional viscous flow, Laminar and turbulent flow in pipes and
ducts, Pipe flow problems, Flow in open channels.
Dimensional Analysis: Buckingham- Pi Theorem, Reynolds’ Law of Similitude,
geometrical, kinematic and, dynamic similarity and related problems.
Fluid Measurements: Measurement of static pressure, Stagnation pressure, flow
velocity and flow rate measurement including Venturimeter, orifice meter, nozzle meter

• Recommend Book(s):
1.Fundamentals of Fluid Mechanics
by Munson, Young & Okiishi, 6th Edition, Wiley
• Reference Book(s):
1.Fluid Mechanics by Frank. M. White, 4th Edition,
McGraw Hill
2.C T Crowe, D F Elger, Engineering Fluid
Mechanics, 9th ed, Wiley, 2008
5

CLO Assessment Mechanism
6
Assessment Module CLO 1 CLO 2 CLO 3
Mid Term (25%) 50% 50% N/A
Assignment / Report/Quiz (15%) 33.3% 33.3% 33.3%
Final Exam (60%) 40% 40% 20%

INTRODUCTION AND
BASIC CONCEPTS

8
INTRODUCTION
Fluid mechanics deals
with liquids and gases in
motion or at rest.
Mechanics: The oldest physical
science that deals with both stationary
and moving bodies under the influence
of forces.
Statics: The branch of mechanics that
deals with bodies at rest.
Dynamics: The branch that deals with
bodies in motion.
Fluid mechanics: The science that
deals with the behavior of fluids at rest
(fluid statics) or in motion (fluid
dynamics), and the interaction of fluids
with solids or other fluids at the
boundaries.
Fluid dynamics: Fluid mechanics is
also referred to as fluid dynamics by
considering fluids at rest as a special
case of motion with zero velocity.

9
Hydrodynamics: The study of the motion of fluids
that can be approximated as incompressible (such as
liquids, especially water, and gases at low speeds).
Hydraulics: A subcategory of hydrodynamics, which
deals with liquid flows in pipes and open channels.
Gas dynamics: Deals with the flow of fluids that
undergo significant density changes, such as the flow
of gases through nozzles at high speeds.
Aerodynamics: Deals with the flow of gases
(especially air) over bodies such as aircraft, rockets,
and automobiles at high or low speeds.
Meteorology, oceanography, and hydrology: Deal
with naturally occurring flows.

10
What is a Fluid?
Matter
Matter exist in two principle forms:
Solid and Fluid
Fluid: A substance in the liquid or gas phase.
A solid can resist an applied shear stress by deforming.
A fluid deforms continuously under the influence of a shear stress, no
matter how small.

11
What is a Fluid?
In solids, stress is proportional to strain, but in fluids, stress is
proportional to strain rate.
When a constant shear force is applied:
a solid eventually stops deforming at some fixed strain angle,
whereas
a fluid never stops deforming and approaches a constant rate of strain.

12
Application Areas of Fluid Mechanics
Fluid dynamics is used extensively
in the design of artificial hearts.
Shown here is the Penn State
Electric Total Artificial Heart.

15
The Wright brothers take flight at Kitty Hawk.
Old and new wind turbine
technologies north of Woodward,
OK. The modern turbines have 1.6
MW capacities.

16
• Property: Any characteristic of a
system.
• Some familiar properties are
pressure P, temperature T, volume
V, and mass m.
• Properties are considered to be
either intensive or extensive.
• Intensive properties: Those that
are independent of the mass of a
system, such as temperature,
pressure, and density.
• Extensive properties: Those
whose values depend on the size—
or extent—of the system.
• Specific properties: Extensive
properties per unit mass.
Criterion to differentiate intensive
and extensive properties.
PROPERTIES OF FLUIDS

17
DENSITY AND SPECIFIC GRAVITY
Density is
mass per unit
volume;
specific volume
is volume per
unit mass.
Specific gravity: The ratio
of the density of a
substance to the density of
some standard substance
at a specified temperature
(usually water at 4°C).
Density
Specific weight: The
weight of a unit volume
of a substance.
Specific volume

Ex: Find SGHg,
If 𝛾𝐻𝑔 = 133
𝐾𝑁
𝑚3 @ 𝑇 = 20 𝐶 (Ans: 13.6)
18

Ideal Gas Law
• Gases are highly compressible than liquids.
• Change in the gas density is directly related to
the change in pressure and temperature through
equation of ideal gas.
𝑃 = 𝜌𝑅𝑇
Where P is the absolute pressure, T is absolute
temperature and R is a gas constant.
• Ideal gas equation is also known as equation of
state.
19

20
Density of Ideal Gases
Equation of state: Any equation that relates the pressure,
temperature, and density (or specific volume) of a substance.
Ideal-gas equation of state: The simplest and best-known
equation of state for substances in the gas phase.
Ru: The universal gas constant
The thermodynamic temperature scale in the SI is the Kelvin scale.
In the English system, it is the Rankine scale.

21
An ideal gas is a hypothetical substance that obeys the relation Pv = RT.
The ideal-gas relation closely approximates the P-v-T behavior of real gases at
low densities.
At low pressures and high temperatures, the density of a gas decreases and the
gas behaves like an ideal gas.
In the range of practical interest, many familiar gases such as air, nitrogen,
oxygen, hydrogen, helium, argon, neon, and krypton and even heavier gases such
as carbon dioxide can be treated as ideal gases with negligible error.
Dense gases such as water vapor in steam power plants and refrigerant vapor in
refrigerators, however, should not be treated as ideal gases since they usually
exist at a state near saturation.

23
Continuum
• Matter is made up of atoms that are widely spaced in the gas phase.
• Yet it is very convenient to disregard the atomic nature of a substance and
view it as a continuous, homogeneous matter with no holes, that is, a
continuum.

24
VISCOSITY
Viscosity: A property that represents the internal resistance of a fluid to
motion or the “fluidity”.
Drag force: The force a flowing fluid exerts on a body in the flow
direction. The magnitude of this force depends, in part, on viscosity
A fluid moving relative to
a body exerts a drag
force on the body, partly
because of friction
caused by viscosity.
The viscosity of a fluid is a
measure of its “resistance to
deformation.”
Viscosity is due to the internal
frictional force that develops
between different layers of
fluids as they are forced to
move relative to each other.

25
The behavior of a fluid in laminar flow
between two parallel plates when the
upper plate moves with a constant velocity.
Consider a fluid between two flat parallel plates.
The bottom plate is rigidly fixed and the upper plate is free to move.
If a force F is applied to the upper plate it will move continuously with a
velocity U.

26
• A close inspection reveals that the fluid in contact with the
upper plate moves with plate velocity U, and the fluid in
contact with the bottom (fixed) plate has zero velocity.
• The fluid between the plates moves with velocity u = u(y).
• For any fluid layer of velocity u it was observed that
𝐹 𝛼 𝐴 (Upper plate Area)
𝐹 𝛼 𝑈 (Upper plate Velocity)
𝐹 𝛼
1
𝑦
(Vertical distance from bottom plate to
the fluid layer)

27
The behavior of a fluid in laminar flow
between two parallel plates when the upper
plate moves with a constant velocity.
Newtonian fluids: Fluids for
which the rate of deformation is
proportional to the shear
stress.
Shear
stress
Shear force

28
In above equation:
du/dy is called the rate of shear strain (𝛾)
µ is the constant of proportionality known as absolute
viscosity, dynamic viscosity or simply viscosity of fluid.
The value of µ depends on the fluid and for any particular
fluid the value of µ depends on the temperature.
 coefficient of viscosity
Dynamic (absolute) viscosity
kg/m  s or N  s/m2 or Pa  s
1 poise = 0.1 Pa  s

29
The rate of deformation (velocity gradient)
of a Newtonian fluid is proportional to
shear stress, and the constant of
proportionality is the viscosity.
Variation of shear stress with the rate
of deformation for Newtonian and
non-Newtonian fluids (the slope of a
curve at a point is the apparent
viscosity of the fluid at that point).

30
Types of Non-Newtonian Fluids:
For shear thinning fluids the apparent viscosity decreases with
increasing shear rate—the harder the fluid is sheared, the less
viscous it becomes.
For example, latex paint Clay, milk, cement)
For shear thickening fluids the apparent viscosity increases with
increasing shear rate—the harder the fluid is sheared, the more
viscous it becomes.
Common examples of this type of fluid include water–corn starch
mixture and water–sand mixture (―quicksand‖). Thus, the difficulty
in removing an object from quicksand increases dramatically as the
speed of removal increases.
Bingham Plastic: It is neither a fluid nor a solid. Such material can
withstand a finite shear stress without motion (therefore, it is not a
fluid) but once the yield stress is exceeded it flows like a fluid
(hence it is not a solid). Toothpaste and mayonnaise are common
example of Bingham plastic materials.

31
Dynamic viscosity, in general,
does not depend on pressure,
but kinematic viscosity does.
Kinematic viscosity
m2/s or stoke
1 stoke = 1 cm2/s
For liquids, both the dynamic and
kinematic viscosities are practically
independent of pressure, and any small
variation with pressure is usually
disregarded, except at extremely high
pressures.
For gases, this is also the case for
dynamic viscosity (at low to moderate
pressures), but not for kinematic
viscosity since the density of a gas is
proportional to its pressure.

32
The viscosity of liquids decreases
and the viscosity of gases
increases with temperature.
The viscosity of a fluid is directly related to
the pumping power needed to transport a
fluid in a pipe or to move a body through a
fluid.
Viscosity is caused by the cohesive forces
between the molecules in liquids and by
the molecular collisions in gases, and it
varies greatly with temperature.
In a liquid, the molecules possess more
energy at higher temperatures, and they
can oppose the large cohesive
intermolecular forces more strongly. As a
result, the energized liquid molecules can
move more freely.
In a gas, the intermolecular forces are
negligible, and the gas molecules at high
temperatures move randomly at higher
velocities. This results in more molecular
collisions per unit volume per unit time and
therefore in greater resistance to flow.

33
The variation of
dynamic
(absolute)
viscosity of
common fluids
with
temperature at
1 atm
(1 Ns/m2
= 1 kg/ms
= 0.020886
lbfs/ft2)

36
A thin 40-cm × 40-cm flat plate is pulled at 2 m/s horizontally through a 3.6-mm-
thick oil layer sandwiched between two plates, one stationary and the other
moving at a constant velocity of 0.3 m/s, as shown in Fig.
The dynamic viscosity of oil is 0.027 Pa·s. Assuming the velocity in each oil layer
to vary linearly,
(a) plot the velocity profile and find the location where the oil velocity is zero and
(b) determine the force that needs to be applied on the plate to maintain this
motion.

37
Consider a point O at a distance of x from the moving wall where
the velocity is zero
By symmetric triangles below the thin plate
Force on upper side
Force on lower side
Total Force required: Fupper + Flower

Calculate the dynamic viscosity of an oil, which is used for
lubrication between a square plate of size 0.8 m x 0.8 m and an
inclined plane with angle of inclination 30o as shown in Fig. The
weight of the square plate is 300 N and it slides down the
inclined plane with a uniform velocity of 0.3 m/s. The thickness
of oil film is 1.5 mm.
Fig.1.4
38

40
This equation can be used to calculate the viscosity of a
fluid by measuring torque at a specified angular velocity.
Therefore, two concentric cylinders can be used as a
viscometer, a device that measures viscosity.
L length of the cylinder
number of revolutions per unit time

42
COMPRESSIBILITY OF
FLUIDS
Coefficient of Compressibility
Fluids, like solids, compress when
the applied pressure is increased
from P1 to P2.
We know from experience that the volume
(or density) of a fluid changes with a
change in its temperature or pressure.
Fluids usually expand as they are heated or
depressurized and contract as they are
cooled or pressurized.
But the amount of volume change is
different for different fluids, and we need to
define properties that relate volume
changes to the changes in pressure and
temperature.
Two such properties are:
the bulk modulus of elasticity 
the coefficient of volume expansion .

43
Coefficient of compressibility
(also called the bulk modulus of
compressibility or bulk modulus of
elasticity) for fluids
The coefficient of compressibility represents the change in pressure
corresponding to a fractional change in volume or density of the fluid
while the temperature remains constant.
What is the coefficient of compressibility of a truly incompressible
substance (v = constant)?
A large value of  indicates that a large change in pressure is needed
to cause a small fractional change in volume, and thus a fluid with a
large  is essentially incompressible.

44
The coefficient of compressibility of an ideal gas is equal to its
absolute pressure, and the coefficient of compressibility of the gas
increases with increasing pressure.
The percent increase of density of an ideal gas during isothermal
compression is equal to the percent increase in pressure.
Isothermal compressibility: The inverse of the coefficient of
compressibility.
The isothermal compressibility of a fluid represents the fractional change
in volume or density corresponding to a unit change in pressure.

45
Coefficient of Volume Expansion
Natural convection over a
woman’s hand.
The density of a fluid depends more
strongly on temperature than it does on
pressure.
The variation of density with
temperature is responsible for
numerous natural phenomena such as
winds, currents in oceans, rise of
plumes in chimneys, the operation of
hot-air balloons, heat transfer by natural
convection, and even the rise of hot air
and thus the phrase “heat rises”.
To quantify these effects, we need a
property that represents the variation of
the density of a fluid with temperature at
constant pressure.

46
The coefficient of volume expansion
(or volume expansivity): The variation of
the density of a fluid with temperature at
constant pressure.
The volume expansion coefficient of an ideal
gas (P = RT ) at a temperature T is
equivalent to the inverse of the temperature:
A large value of  for a fluid means a large
change in density with temperature,
and the product  T represents the fraction of
volume change of a fluid that corresponds to a
temperature change of T at constant pressure.
The coefficient of volume expansion
is a measure of the change in
volume of a substance with
temperature at constant pressure.

47
Cohesion and Adhesion:
In liquids, molecule is attracted equally in all directions by other like
molecules surrounding it ---- This is called Cohesion.
Cohesive forces are the force of attraction between like neighboring molecules.
The force of attraction between the molecules of two different liquids or a
liquid and a solid is called adhesion OR Adhesive forces are force of
attraction between two dislike molecules e.g. a liquid and a solid surface.
Wetting and Non wetting Liquids:
Wetting liquids are those which wet the solid surface when comes in contact
with it. The adhesive force (i.e. the force of attraction between molecules of
solid surface to molecules of liquid surface) is higher than that of cohesive
force. The angle of contact (θ) in wetting liquid is less than 90 degree.
Non-wetting liquids are those which does not wet the solid surface when
comes in contact with it. In this type of liquids, the cohesive force is greater
than adhesive force. The angle of contact (θ) in non-wetting liquid is greater
than 90 degree.

48
SURFACE TENSION AND
CAPILLARY EFFECT
Some consequences of surface tension: (a) drops of water beading
up on a leaf, (b) a water strider sitting on top of the surface of water,
and (c) a color schlieren image of the water strider revealing how
the water surface dips down where its feet contact the water (it
looks like two insects but the second one is just a shadow).
• Liquid droplets behave like small balloons filled
with the liquid on a solid surface, and the surface
of the liquid acts like a stretched elastic membrane
under tension.
• The pulling force that causes this tension acts
parallel to the surface and is due to the attractive
forces between the molecules of the liquid.
• The magnitude of this force per unit length is called
surface tension (or coefficient of surface tension)
and is usually expressed in the unit N/m.
• This effect is also called surface energy [per unit
area] and is expressed in the equivalent unit of N 
m/m2.

49
Attractive forces acting on a liquid
molecule at the surface and deep
inside the liquid.
Stretching a liquid film with a U-
shaped wire, and the forces acting
on the movable wire of length b.
Surface tension: The work done per unit
increase in the surface area of the liquid.

50
The free-body
diagram of half a
droplet or air
bubble and half
a soap bubble.

Find the surface tension in a soap bubble of 40 mm
diameter when the inside pressure is 2.5 N/m2 above
atmospheric pressure.
51

52
Capillary Effect
Capillary effect: The rise or fall of a liquid in a small-diameter tube inserted into the
liquid.
Capillaries: Such narrow tubes or confined flow channels.
The capillary effect is partially responsible for the rise of water to the top of tall trees.
Meniscus: The curved free surface of a liquid in a capillary tube.
The contact angle for wetting and
nonwetting fluids.
The meniscus of colored water in a
4-mm-inner-diameter glass tube.
Note that the edge of the meniscus
meets the wall of the capillary tube
at a very small contact angle.
The strength of the capillary effect is
quantified by the contact (or wetting)
angle, defined as the angle that the
tangent to the liquid surface makes with
the solid surface at the point of contact.

53
The capillary rise of water and the
capillary fall of mercury in a small-
diameter glass tube.
The forces acting on a liquid column
that has risen in a tube due to the
capillary effect.
 Capillary rise is inversely proportional to the
radius of the tube and density of the liquid.

basic concepts of fluid mechanics (FM-1).pdf

More Related Content

What's hot (20)

Similar to basic concepts of fluid mechanics (FM-1).pdf (20)

More from FaizanAhmed396943 (8)

Recently uploaded (20)

basic concepts of fluid mechanics (FM-1).pdf