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INTRODUCTION & BASICCONCEPT
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INTRODUCTION:Mechanics:
Stationary & moving bodies subjected to forces
Statics:
At rest(stationary)
Dynamics:
In motion(moving)
Fluid Mechanics:
Behaviour of fluids & interaction ofsolids & other fluids at the boundaries
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INTRODUCTION:
Fluid Mechanics
Gas dynamics:
Fluids that undergo density changes
Meteorology; oceanography & hydrology:
Naturally occurring flows
Aerodynamics:
Gas flows over bodies at high/low speeds
Hydrodynamics:
Motion of incompressible fluids
Hydraulics:
Liquid flows in pipes &open channels
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WHAT IS A FLUID?: Fluids:
A substance in the liquid or gas phase.
The differences between solid & liquid:
Solid Liquid
Can resist applied shear stress by
deforming
Deforms continuously due to even the
smallest shear stress
Stress proportional to strain Stress proportional to strain rate
Stops deforming when a constant
shear force is applied (at fixed strain
angle)
Never stop deforming and approaches
a certain rate of strain
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WHAT IS A FLUID?:
In a fluid at rest,
the normal stress is called as Pressure.
Zero shear stress.
AAreaFForceofcomponentTangentialstressShear
AArea
FForceofcomponentNormalstressNormal
t
n
,,,
,
,,
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WHAT IS A FLUID?: Solids & fluids may not be so clear in some borderline cases
e.g. asphalt (resist shear stress for a while; deforms slowly if
forces exerted over extended period of time), some plastics,
lead & slurry mixtures. [beyond the scope!]
Fluids that are dealt in this course are easily recognizable.
Intermolecular bonds are strongest in solids, but weakest in
gas [Reason: in solids, molecules are closely packed together].
Because the small distance between molecules in solids
attractive forces are large & keep molecules at fixed position.
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WHAT IS A FLUID?: Molecule spacing in liquids are somewhat similar with solids,
except molecules are not in fixed position & can rotate freely.
The distance between molecules generally increase slightly as
solids turns liquid [e.g. water].
Gas molecules moves at random, collides with each other &
the walls of the container which they are confined.
Molecules at gas phase are at higher energy level; must
release large amount of energy before it can condense or
freeze.
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WHAT IS A FLUID?: Gas & vapour are often used synonymously:
Gas: A vapour phase of a substance when above the critical
temperature.
Vapour: The current phase is not far from a state of
condensation.
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APPLICATION AREAS:
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THE NO-SLIP CONDITION: Fluid flow are often confined by solid surfaces important to
understand how these solid surfaces affects fluid flow.
Consider the flow of a fluid in a stationary pipe/over a solid
impermeable surface.
All experimental observations indicate that a fluid in motion
comes to a complete stop at the surface (assumes zero
velocity to the surface).
That is, a fluid is in direct contact with the a solid sticks to
the surface [no slip].
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THE NO-SLIP CONDITION:
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THE NO-SLIP CONDITION: Viscosity is responsible for the no-slip condition & the
development of boundary layer.
The no-slip condition is also responsible for the development
of the velocity profile.
Boundary layer: the flow region where the viscous effects (and
the velocity gradient) are significant.
No-slip conditions also responsible for the surface dragor skin
friction drag.
If a fluid is forced to flow over a curved surface, the boundary
layer no longer attached to the surface & separate from the
surfaceflow separation.
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THE NO-SLIP CONDITION:The Velocity Profile: Flow Separation:
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CLASSIFICATION OF FLUID FLOWS:
Classificationof Fluid
Flows
Viscous vs. InviscidRegions of Flow
Compressible vs.Incompressible flow
Laminar vs. Turbulent
Steady vs. UnsteadyFlow
1-, 2- & 3-dimensional Flows
Internal vs. ExternalFlow
Natural (Unforced) vs.Forced Flow
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VISCOUS VS. INVISCID: The development of viscous & inviscid regions of flow can
be seen by inserting a flat plate parallel into a fluid stream
of uniform velocity.
The fluid sticks to the plate on both sides because of the
no-slip condition.
Viscous flow region: The thin boundary layer in which the
viscous effects are significant (near the plate) Inviscid flow region: The region of flow on both sides
away from the plate and affected by the plate.
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VISCOUS VS. INVISCID:
INVISCID INVISCIDVISCOUS
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COMPRESSIBLE VS.
INCOMPRESSIBLE FLOW: Incompressibility: an approximation in which a flow is said to
be incompressible if the density remains nearly constant
throughout.
Volume remains unchanged when the flow is incompressible.
The densities of liquids are constant, thus liquid is typically
incompressible. [incompressible substance].
Gases are highly compressible. Modelling gas flows as
incompressible depends on the Mach number, usually the case
when Ma < 0.3.
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COMPRESSIBLE VS.
INCOMPRESSIBLE FLOW: Mach number,
Small density changes of liquid corresponding to large
pressure changes still have important consequences, e.g.
water hammer.
soundofSpeed
flowofSpeed
c
VMa
Ma = 1 Sonic
Ma < 1 Subsonic
Ma > 1 Supersonic
Ma >> 1 Hypersonic
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LAMINAR VS. TURBULENT: Laminar: The highly ordered fluid motions characterized
by smooth layers.
The flow of high-viscosity fluids (e.g. oil) at low velocities
are typically laminar.
Turbulent: The highly disordered fluid motions that
typically occurs at high velocities.
Transitional: A flow that alternates between beinglaminar and turbulent.
Reynolds number, Re: the key parameter for the
determination of flow regimes in pipes.
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LAMINAR VS. TURBULENT:
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NATURAL VS. FORCED FLOW: Forced Flow: A fluid is forced to flow over a surface or in
a pipe by external means e.g. pump or fan.
Natural/Unforced Flow: Fluid motion is due to natural
means e.g. the bouyancy effect (the rise of warmer &
lighter fluid and the fall of cooler & denser fluid).
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STEADY VS. UNSTEADY FLOW: Steady: No change at a point of time.
Unsteady: Change at a point of time (opposite ofsteady).
Uniform: No change with location over a specified region. Non-uniform: Change with location over a specified
region.
Transient: developing flows.
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1-, 2- & 3-DIMENSIONAL FLOWS A flow field is best characterized by its velocity
distribution.
A flow is said to be one-, two-, or three-dimensional if the
flow velocity varies in one, two, or three primary
dimension, respectively.
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SYSTEM & CONTROL VOLUME: System: A quantity of matter / a region in space chosen
for study.
Surroundings: The mass/region outside the system.
Boundary: The real/imaginary surface that separates the
system from its surroundings. Can be fixed or moveable.
SYSTEM
SURROUNDINGS
BOUNDARY
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SYSTEM & CONTROL VOLUME: Closed system (or control mass):
consists of a fixed amount of mass, and no mass can cross
the boundary.
Energy can cross the boundary & the volume of a closed
system does not have to be fixed.
Isolated system: If even energy is not allowed to cross the
boundary.
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SYSTEM & CONTROL VOLUME: Open system (or control volume):
encloses a device that involves mass flow e.g. compressor,
turbine or nozzle.
Flow through these device is studied by selecting the region
within a device as the control volume.
Both mass & energy can cross the boundary (the control
surface)
CV
(a nozzle)
Imaginary
boundary
Real
boundary
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IMPORTANCE OF DIMENSIONS
AND UNITS: Any physical quantity can be characterized by dimensions.
The magnitude assigned to the dimensions are called units.
Some basic dimensions e.g. mass m, length L, time tare called
primary/fundamental dimensions.
Velocity V, and energy Eare expressed in terms of primary
dimensions are called secondary/derived dimensions.
Two sets of units are still in common use today: the English
system(United States Customary System, USCS), and the
metric SI (Le Systme International dUnits), also known as
International System.
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IMPORTANCE OF DIMENSIONS
AND UNITS: The SI:
is a simple & logical based on a decimal relationshipbetween various units.
is used for scientific & engineering work in most of theindustrialized nations, including England.
The English system:
has no systematic numerical base; various units in this
system are related to each other rather arbitrarily. confusing & difficult to learn.
The United States is the only industrialized country usingthis system.
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IMPORTANCE OF DIMENSIONS
AND UNITS:The seven fundamental (or primary) dimensions and their
units in SIDimension Unit
Length Meter (m)
Mass Kilogram (kg)
Time Second (s)
Temperature Kelvin (K)
Electric current Ampere (A)Amount of light Candela (cd)
Amount of matter Mole (m)
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DIMENSIONAL HOMOGENEITY: In engineering, all equations must be dimensionally
homogeneous: every term in an equation must have the
same dimensions.
If two quantities that have different dimensions (or units)
are added, it is an indication that error is made.
Thus,
ALWAYSCHECK THE UNITS IN YOUR CALCULATIONS!!
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UNITY CONVERSION RATIOS: Take for example:
They can also be expressed more conveniently as unity
conversion ratios:
If a box of breakfast cereal written as net weight = 454 g, theactual weigh of the cereal on earth is:
2s
mkgN
1/
2
smkg
N
Ng
kg
smkg
NsmgmgW 49.4
1000
1
/.1
1)/81.9)(6.453(
2
2