MTH- 486: Fluid Mechanics
Instructor:
Dr. Fahad Munir Abbasi
Assistant Professor
Department of Mathematics
Comsats Institute of Information Technology
Islamabad, Pakistan
Layout of this lecture
Introduction of the instructor
Introduction of the course
Learning outcomes and recommended books
Course evaluation and commonly asked questions
Historical background and importance of fluid mechanics
Some basic definitions
Summary
My introduction
MSc. Mathematics in 2008, from Quaid-i-Azam University,
Islamabad, Pakistan
M.Phil. Mathematics in 2010, from Quaid-i-Azam University,
Islamabad, Pakistan
PhD Mathematics in 2014, from Quaid-i-Azam University,
Islamabad, Pakistan
cont...
Presently, working as Assistant Professor at Department of
Mathematics, CIIT, Islamabad, Pakistan.
Specialization in Newtonian and non-Newtonian fluid
mechanics, Peristaltic flows, Magnetohydrodynamics, Heat
and mass transfer, Analytical and numerical solutions of
D.Es
HEC Indigenous scholar during my PhD, Presently 35
International publications to my credit with total impact factor
> 38.
Course introduction
Course code: MTH-486
Course title: Fluid Mechanics
Credit hours: 03
cont.…
• Basic definitions and concepts
Course
Outlines
(e.g. Different classifications of fluids;
properties of fluids (like density,
viscosity etc.); Eulerian and Langrangian
approach; velocity of a fluid at a point,
streamlines
and
pathlines; flow
classifications;
velocity
potential;
vorticity vector; local and particle rates
of change; Sources, sinks; doublets;
stream lines and stream functions etc.)
cont.…
• Fundamental
governing
Course
Outlines
laws
and
equations
(e.g. Law of conservation of mass, law
of conservations of momentum, energy
conservation laws, The basic hydrostatic
equation; The continuity equation, The
Euler’s equation of motion, The
Bernoulli's equation, The Navier-Stokes
equation etc.)
cont.…
• Applications
Course
Outlines
(e.g. in Poiseuille flow; Couette flow;
Unsteady unidirectional low; sudden
motion of a plane boundary in a fluid at
rest; Flow due to an oscillatory
boundary; i.e. Stokes problems etc. )
cont.…
• Some fundamental theorems
Course
Outlines
(e.g. Miline-Thomson circle theorem;
Blasius’ theorem, Kelvin’ s minimum
energy theorem; Uniqueness theorem
etc. )
Learning outcomes
What we are
aiming for?
• This first course in fluid mechanics
familiarizes the student with the
basic definitions, fundamental laws
and equations and some of the basic
techniques for the analysis of fluid
behavior.
• At the end of this course the students
will have a good working knowledge
of the basic concepts related to fluids
mechanics, techniques and equations
governing the fluid motion.
Recommended books
Books related
to this course:
• White, F. M., Introduction to Fluid
Mechanics, 4th Edition, MacGraw-Hill,
2014.
• Chorlton, F., Textbook of fluid Dynamics,
D. Van Nostrand Co. Ltd. 1967.
• Thomson, M., Theoretical
Hydrodynamics, Macmillan Press, 1979.
• Landau, L.D., and Lifshitz, E.M., Fluid
Mehanics, Pergamon Press, 1966.
• Batchelor, G.K., An Introduction to Fluid
Dynamics, Cambridge University Press,
1969.
Course evaluation
• Quizzes
Evaluation
will include:
• Assignments
• Sessional exams
• Terminal exam
Commonly asked questions
Why fluid
mechanics?
• Occurrence (from inter-cellular to interstellar space you will find fluid
everywhere, it is in our veins, our
arteries, within the body of all living
beings, in our houses, at our offices, in
the atmosphere, even in our tears)
• Utility
and
applications
(better
understanding of the subject can prove
very helpful in facilitating us in all forms
of life)
• Wide scope of research for students
willing to pursue to MPhil and PhD.
• It is very interesting and grasping
subject.
cont.…
• The answer is “NO”.
Is prior
knowledge of
physics
mandatory?
• Although better understanding of physics
may
prove
fruitful
in
better
understanding of the subject, yet it is not
mandatory.
• Since we will be perusing this course
from mathematical point of view so it is
really not difficult for those students who
haven't studied physics at the
intermediate level.
• The mathematical results which we will
derive will speak for their physical
interpretation them self and we will
explain things in a simple manner so that
you can understand it well
cont.…
• A wise man once said that “there is no
How to peruse
this course in
order to get
best out of it?
simpler way of doing mathematics than
DOING IT”.
• CRAMMING isn’t the, key PRACTICE is.
• Try to learn mathematics instead of
memorizing it.
Last words, before the start
• After every lecture, try to reproduce
what you have learnt in your own words
and do all the mathematics by yourself.
Tips for our
students:
• Never feel hesitant to ask questions,
there is not better time for you to learn
fluid mechanics.
• Feel free to communicate, we are here
to help.
MTH- 486: Fluid Mechanics
Instructor:
Dr. Fahad Munir Abbasi
Starting from what you already know
• Matter: Matter has many definitions,
but the most common is that it is any
substance which has mass and occupies
Reminders
space. All physical objects are composed
of matter, in the form of atoms, which
are in turn composed of protons,
neutrons, and electrons.
cont.…
• States of Matter:
Reminders
Matter can exist in various
states/phases: solid, liquid, gas, or
plasma. Most substances can transition
between these phases based on the
amount of heat the material absorbs (or
loses).
• States of Matter: Gases, liquids and
solids are all made up of microscopic
particles, but the behaviors of these
particles differ in the three phases.
cont.…
Fluid Mechanics
Fluid
+
Mechanics
cont.…
Fluid
• Anything that can flow can be named as
fluid e.g. water, air, blood, urine, lava,
paints, lubricants etc.
• To be more precise “anything that
deforms continuously and indefinitely
under the action of applied stress is
called Fluid ”
• from the examples quoted above you
can see that water is different from air,
but since both can flow so both are
fluids, but surely of different types
(which we will soon study in detail).
cont.…
Mechanics
• The branch of physics that deals with
the action of forces on any substance. It
further has two branches, namely,
Statics and Dynamics. Statics: Study of
the effects of forces on a body at rest;
Dynamics: Study of the effects of forces
on a body in motion.
• Celestial mechanics, the motion of
bodies in space: planets, comets, stars,
galaxies, etc.
• Soil mechanics, mechanical behavior of
soils
Historical background
Some
glimpses
through
history
• Development of the subject of fluid
mechanics started even before the birth
of Christ. It took hundred of years and
life time inputs of countless scientists to
make this subject reach where it stands
today. Out of those numerous
researches some are mentioned here as
an
acknowledgement
to
their
contribution to this field:
• Archimedes (287-212 B. C.) for his
famous Buoyancy principle.
• Benito Castelli (1577-1644) for his work
on continuity principle.
cont.…
Some
glimpses
through
history
• Blaise Pascal (1623-1662) for his work
on pressure for static fluids.
• Sir Issac Newton (1642-1727) for his
resistance law for fluids.
• Daniel Bernoulli (1700-1782) for his well
known Bernoulli’s equation.
• Leonhard Euler (1707-1783) for his
famous Euler’s equation.
• Navier (1785-1836) and Stokes (18191903) for their famous Navier-Stokes
equations.
• Osborne Reynolds (1842–1912) for his
work on turbulent flows.
cont.…
Some
glimpses
through
history
• Ludwig Prandtl (1875 – 1953) with his
boundary layer theory, not only
answered many questions from the past
but also opened new ways for the future
research and developments in the field
of fluid mechanics.
• For further details you can concern the
books mentioned in the introduction of
this lecture.
Importance of fluid mechanics
Applications
• Aeronautics and astronautics: aircraft
and missile aerodynamics, designing
and applications of satellites, control
hydraulics etc.
• Civil engineering: pipe and channel
flows, surface and ground water
hydrology, designing of wind and water
structures, water and waste treatments
etc.
• Physics: treatment of corrosive and
sensitive
fluids,
hydro
and
magnetohydrodynamics,
super
conductors,
cont.…
Applications
• Astrophysics: interstellar gas dynamics,
solar winds and comet tails etc.
• Biology: blood flow, urine transport,
breathing aids, surgical processes,
heart-lung and dialysis machines, drug
delivery systems etc.
• Mechanical and Nuclear engineering:
pumps
and
compressors,
heat
exchangers, heating and cooling systems
etc.
• Geophysics: Metrology, oceanography,
geo-magnetism, glacier flows etc.
• Any many others…
Fluid mechanics: basic definitions
Quantities
we will look
for:
• IT is worth mentioning that state of the
fluid can be completely determined with
the aid of five quantities: Three
components of the velocity V(x, y, z), the
pressure P (x, y, z) and the density ρ (x,
y, z).
cont.…
Basic laws
and
principles
•
•
•
•
•
Law of conservation of mass
Newton’s second law (F = ma)
Law of conservation of momentum
First law of thermodynamics
Second law of thermodynamics
cont.…
Velocity
field
• We define the velocity of the fluid at any point “c”
as the instantaneous velocity of the fluid particle
that is passing through that point at the given
instant of time. At a given instant, the velocity
field, V is a function of the space coordinates x, y
and z. The velocity of the fluid at any point varies
from instant to instant. Therefore, the complete
representation of velocity field is given by V = V (x,
y, z, t).
• The velocity vector V can be written in terms of
three scalar components. Denoting the
components in the x, y and z directions as u, v and
w, then V = u i + v j + w k .
cont.…
Density
• The mass per unit volume (for a 3-D object) at
a given temperature and pressure, or stress
conditions and is expressed by the relation
ρ = m/V
Specific
weight
• Weight of a unit volume, γ = ρg
Specific
volume
• Volume of a unit mass = 1/ρ
cont.…
Rate of
discharge
• The quantity of a fluid, flowing per second,
through a section of a pipe or a channel, is
known as the rate of discharge or simply
“discharge”. In general it is denoted by Q.
• Now consider a liquid flowing through a
pipe. If “a” denotes the cross sectional area
of the fluid and “V” the average velocity of
the fluid, then
discharge = Area X average velocity
or
Q = a X V.
Summary of the lecture
Introduction of this course and the instructor
Historical background and importance of fluid mechanics
Some important and basic definitions
Today’s quote:
A man is honored, proportional to the
knowledge he has.