FLUID

• Recommended Books:
 “Fluid Mechanics with Engineering
Applications” 10th Edition
By: E. John Finnemore & Joseph B.
Franzini
 “Fluid Mechanics with Engineering
Applications” SI Metric edition
By: Robert L. Daugherty, Joseph B.
Franzini & E. John Finnemore
 “Fundamentals of Fluid Mechanics”
FLUID MECHANICS-I By: Musen Young

** Useful links:
Engr. AURANGZEB • http://www.civil.canterbury.ac.nz/
00923459026940 pubs/FM4CE.pdf

Prepared by: Engr. Fazal-E-Jalal Fluid Mechanics-I 1

COURSE CONTENTS

1. Introduction
2. Fluid Statics
3. Forces on Immersed bodies
4. Fluid Kinematics
5. Hydrodynamics
6. Flow measurement
7. Steady Flow through pipes
8. Uniform flow in open channels
9. Dimensional Analysis and Similitude


LECTURE# 01


Contents
• Scope of Fluid Mechanics
1. Applications
2. Branches of Fluid mechanics
3. Advancement with advent of computers
• Dimensions and Units
1. British Gravitational System
2. System International
3. Scope of above mentioned systems


Scope of Fluid Mechanics
• Fluid Mechanics is involved in:
1. Movement of clouds in atmosphere
2. Flight of birds through air
3. Flow of water in streams
4. Breaking of waves at seashore
• F.M include “gases” and “liquids”, with air
and water as most prevalent.


• Some other aspects that include F.M are:
 Flow in pipelines and channels
 Movements of air and blood in body
 Air resistance or Drag
 Wind loading on buildings
 Motion of projectiles, jets, shock waves
 Lubrication


 Combustion
 Irrigation
 Sedimentation
 Meteorology
 Oceanography


• A knowledge of Fluid mechanics is required to
properly design:
a) Water supply systems
b) Wastewater Treatment facilities
c) Dam Spillways
d) Valves, Windmills, Turbines, Pumps
e) Flow meters, Heating & Air-conditioning system
f) Hydraulic shock absorbers and brakes


g) Automatic transmissions
h) Aircrafts, Ships, Submarines
i) Windmills, Turbines, Pumps etc.
It is clear that every body’s life is affected by
Fluid mechanics in variety of ways. All
engineers should have at least a basic
knowledge of fluid phenomenon.


A substance which is Interaction of forces
capable of flowing
More about Fluids….
They have no definite Ideal fluids are those that
have no viscosity and
shape of their own but A fluid may be in liquid or surface tension and they are
conforms to the shape of gaseous form. compressible. In practice
containing vessel such fluids don’t exist.


Fluid Mechanics is the science of mechanics of liquids
and gases, and is based on the same fundamental
principles that are employed in the mechanics of
solids.

The mechanics of fluids is more complicated subject
than mechanics of solids, however, because with
solids one deals with separate and tangible
elements, while with fluids there are no separate
elements to be distinguished.


2. Kinematics

1. Fluid Statics 3. Fluid Dynamics

FLUID
MECHANICS


Fluid Statics is the study
of mechanics of fluids at
REST.

Fluid Dynamics
Kinematics deals
deals with velocities
with velocities and
& accelerations and
streamlines without
forces exerted by or
considering FORCES
upon fluids in
or ENERGY.
MOTION.


• HYDRODYNAMICS: In mathematics, it is a
subject that deals with an imaginary ideal fluid
that is completely frictionless.
• When dealing with liquids, this subject is
called HYDRAULICS.
• Ideal fluids + Real fluids = Fluid Mechanics
Ideal: Hydrodynamics
Real: Liquids (Hydraulics) and gases

Dimensions and Units
• To properly define a physical property or a
fluid phenomenon, one must express the
property or phenomenon in terms of some
sets of units.
For example, the diameter of a pipe might be 160 mm
and the average flow velocity 8 m/s. A different sets of
units might have been used, such as diameter of 0.16 m
and velocity of 800 cm/s.


• Modern Fluid Mechanics: The basic principles
of hydrodynamics are combined with
experimental data.
With advent of computer, during last couple of decades
the entirely new field of COMPUTATIONAL FLUID
DYNAMICS has been developed.
Various numerical methods such as Finite
differences, Finite elements, Boundary elements and
Analytical elements are now used to solve problems in
Fluid mechanics.


• We will be dealing with two systems of units:
1. English Units (British Gravitational i.e. BG System or
US Customary System or FPS System)
2. Metric Units (Systeme Internationale d’ Unites i.e.
S.I System)

Because English units have been used in the technical
literature for so many years and as S.I system, nowadays, is
been used by almost every country all over the world; it is
essential for engineer to be familiar with both the systems.

• In fluid mechanics, the basic dimensions are:
1. Length (L)
2. Mass (M)
3. Time (T)
4. Force (F)
5. Temperature (Ѳ)
First three are the basic units e.g. In F = ma , “a” i.e.
acceleration is expressed by its basic dimensions as LT-2

In the two systems of units that we will be dealing, the
commonly used units for the basic five dimensions are:

Dimension BG System SI Unit
Length (L) Foot (ft) Meter (m)

Mass (M) Slug ( = lb.sec2/ft) Kilogram (kg)

Time (T) Second (sec) Second (sec)

Force (F) Pound (lb) Newton (N) (= kg.m/s2)

Temperature (Ѳ)

Absolute Rankine (°R) Kelvin (K)

Ordinary Fahrenheit ( °F) Celsius ( °C)


• S.I system employs L,M and T and derives F
from MLT-2.
• Force in S.I is defined as NEWTON. Newton is
defined as “ The force required to accelerate
one kilogram of mass at rate of one meter per
second” 1 Newton = (1 kg) (1 m/s2)
• On the other hand, the British Gravitational
system employs L,F and T and derive Mass as
F/a = FL-1T2


• Mass in BG system is defined as SLUG. Slug
can be defined as “ Mass that accelerates at
one foot per second when acted upon by a
force of one pound”
• 1 Slug = (1 lb) (1 ft/sec2) = 1 lb.sec2/ft
• 1 lb = (1 slug)(1 ft/sec2)
We see that the definition of mass in BG system depends on definition of
pound, which is “ The force of gravity acting on a platinum standard whose
mass is 0.45359243 kg.”
Weight is defined as “ The gravitational force F between two bodies of masses
m1 and m2, given by Newton’s law of Gravitation.” F = G.(m1m2)/r2

• Where, “G” is Universal constant of
Gravitation and “r” is distance between the
centers of two masses.
• If “m” is mass of object on earth and “ M” is
mass of earth, then “r” is radius of earth, so
that;
• F = m.(GM)/r2
• Weight of object is; W = m.g
where g = GM/r2

• Clearly, “g” varies slightly with altitude and
latitude on earth, since the earth is not truly
spherical, while in space and in other planets
it is much different.
• Also, the earth’s rotation by centrifugal action
reduces the apparent weight of an object by
at most 0.35 % at the equator.
• Because the force depends on value of “g”,
which in turn varies with location.


• BG system based on Length, Force and Time is
referred as Gravitational system.
• S.I system based on Length, Mass and Time is
Absolute system because it is independent of
the gravitational acceleration “g”.

A partial list of derived quantities encountered in Fluid
mechanics and their commonly used dimensions in
terms of L,M,T & F is:


Quantity Commonly used BG Unit SI Unit
dimensions
Acceleration (a) LT-2 Ft/sec2 m/s2
Area (A) L2 Ft2 m2
Density ML-3 Slug/ft3 Kg/m3
Energy, Work or Heat FL Ft.lb N.m = J
Flow rate (Q) L3T-1 Ft3/sec (cfs) M3/sec
Frequency T-1 Cycles/sec (sec-1) Hz (Hertz, s-1)
Kinematic L2T-1 Ft2/sec M2/sec
Viscosity(ν)
Power FLT-1 Ft.lb/sec N.m/sec = W
Pressure(p) FL-2 Lb/in2 N/m2 = Pa
Specific weight (ɣ) FL-3 Lb/ft3 N/m3
Velocity (V) LT-1 Ft/sec m/s
Viscosity (μ) FTL-2 Lb.sec/ft2 N.s/m2
Volume L3 ft3 m3

• Radians don’t have dimensions, because they
are defined as the arc length divided by
radius.
• On earth’s surface, variation in “g” is very
small and by international agreement, the
standard gravitational acceleration at sea level
is 32.1740 ft/sec2 or 9.80665 m/sec2 (for
problem solving we usually use 32.2 ft/s2 or
9.81 m/s2)


• For unit mass (I slug or 1 kg) on the earth’s
surface, we note that:
• In BG Units; W = mg = (1 slug)(32.2 ft/s2) =
32.2 N
• In S.I Units; W = mg = (1 Kg)(9.81 m/s2) =
9.81 N


• Other systems of units are:
1. English Engineering System (lb-f and lb-m)
2. Absolute Metric System (CGS System)
3. MKS Metric System (Kg-f and Kg-m)
• Both EE & MKS system are “Inconsistent
systems” whereas BG & S.I systems are
“Consistent systems”.
CGS system is both consistent and non gravitational, it is little used for
engineering applications because its unit of force dyne is so small;
1 Prepared by: Engr. Fazal-E-Jalal 2) = 10-5 Newtons.
Dyne = (1g)(1 cm/s Fluid Mechanics-I 28

• Non standard or Traditional abbreviations
used by engineers sometimes e.g.
fps, gpm, cusec etc.
• Acres, Tons, and Slugs are not abbreviated.
• When units are named after people, they are
capitalized. E.g. newton (N), joule (J), pascal
(Pa) etc.
• The abbreviation capital L for liter is a special
case. (to avoid confusion with 1)

• We will use kg for kilogram mass and lb for
pound force. The abbreviation lb for pound is
taken from Latin word “libra”.
• The units second, minute hour, day and year
are correctly abbreviated as s, min, h, d and y
in the S.I system, and although in BG system
they should be abbreviated as sec, min, hr,
day and yr.


• Kelvin (K) is also abbreviated without a
degree.
• UK & US Gallons. UK ( = 4.55 Liters) US (= 3.78
Liters). If not specified, assume the US gallon.
• When dealing with very large or small
numbers, series of prefixes is adopted in S.I
units. e.g. mega, milli, kilo etc.


• Often we need to convert quantities from BG
units into S.I units, and vice versa. Conversion
factors may be used.
In SI units, LENGTHS are commonly expressed in
millimeters, centimeters, meters or
kilometers, depending on the distance being
measured.
AREAS are usually expressed in square cm, square
meters or hectares (ha), depending on the area being
measured. 1 hectare = 10,000 m2 = 2.5 Acres

• 1 N = 0.225 lb
• Units for stress in S.I are N/m2 i.e. Pascal (Pa)
• 1 Pa = 0.021 lb/ft2 = .00015 psi
• Units of Energy is Joule. 1 joule = 1 N.m
• Unit of power is Watt (W). W = J/s = N.m/s
When we have to work with less usual units, like
centipoise (for viscosity) or ergs (for energy), It is best
to convert them into S.I or BG units as soon as
possible.

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