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Lecture Notes on Fluid Mechanics I "Fundamentals of Fluids Mechanics

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Lecture Notes on Fluid Mechanics I 5th Ed. Update by B. R. Munson, D. F. Young, and T. H. Okiishi 1 (2 ) – PowerPoint PPT presentation

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Title: Lecture Notes on Fluid Mechanics I "Fundamentals of Fluids Mechanics


1
Lecture Notes on Fluid Mechanics I 5th Ed.
Update by B. R. Munson, D. F. Young, and T.
H. Okiishi ???????? ???? 1 ????(2??
??) http//www.mecha.ac.kr/down.php
???? http//yoo2.kangwon.ac.kr /lecture T
Text Book 1 "Mechanics of Fluids" 2nd Ed. by
Potter and Wiggert 2 "Fluid Mechanics" 4th
Ed. by F. M. White
Fundamentals of Fluid Mechanics
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CH 1. Introduction
? Fluid Mechanics(????) the study of fluids
in motion or at rest and the subsequent effects
of the fluid on the boundaries, which may be
either solid surfaces or other fluids1
Fluid mechanics is that discipline within the
board field of applied mechanics concerned with
the behavior of liquids and gases at rest or in
motion. 1.1 Some Characteristics of Fluids 1.
Definition of Fluid - a substance that deforms
continuously(flows) when acted on by a shearing
stress of any magnitudeT - a substance which
must continue to change shape(deform) as long as
there is a shear stress present, however small,
i.e., a substance which, when at rest, cannot
sustain a shear stress
6
- those liquids and gases that move under the
action of a shear stress, no matter how small
that shear stress may be. - case of solid A
solid can resist a shear stress by a static
deformation. 2. Fluid Liquid Gas1 1
Liquid 1) definition A state of matter in
which the molecules are relatively free to change
their positions with respect to each other but
restricted by cohesive forces(???) so as to
maintain a relatively fixed volume 2)
characteristics - retain a definite volume in a
container - form a free surface(????) in
gravitational field(???) - strong
intermolecular cohesive force
7
Definition of fluid
- A fluid is a substance that deforms
continuously under the action of an applied shear
force or stress - A fluid is a substance that can
resist shear only when moving
8
- the spacing between molecules at a normal
pressure and temperature order of -
number of molecules per 2 Gas 1) definition
A state of matter in which the molecules are
practically unrestricted by cohesive forces. A
gas has neither definite shape nor volume. 2)
characteristics - volume of gasvolume of
container - Gas cannot form a free surface, and
thus gas flows rarely concerned with
gravitational effects other than buoyancy(??). -
negligible cohesive forces - A gas is free to
expand until it encounters confining walls. - A
gas has no definite volume and left to itself
without confinement forms an atmosphere which is
essentially hydrostatic.
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  • the spacing between molecules at a normal
    pressure and temperature order of
  • number of molecules per
  • 3. Continuum(???)
  • 1 Meaning
  • 1) condition for macroscopic point of view
  • dimension of volume element gtgt molecular
    dimension , i.e., a volume element contains so
    great many molecules
  • 2) continuity
  • - It means that the local variation in
    properties is so smooth(continuous) that the
    differential calculus can be used to analyze the
    substance.
  • - We thus assume that all the fluid
    characteristics we are interested in (pressure,
    velocity, etc.) vary continuously throughout the
    fluid-that is, we treat the fluid as a
    continuum.T

11
2 Characteristics - not concerned with the
behavior of individual molecules - treat the
substance as being continuous no voids, no
holes - assumption that both gases and liquids
are continuously distributed throughout a region
of interest
12
Continuum Hypothesis
All substances are composed of an extremely large
number of molecules. Molecules interact with
each other via collision and intermolecular
forces gt ignore the molecular nature of matter
and assume that the matter is continuous
Continuum hypothesis
13
1.2 Dimensions (??), Dimensional Homogeneity (???
???), and Units (??)
1. Dimension 1 Definition the measure by
which a physical variable is expressed
qualitatively length, mass 2 4 Basic
Dimensions(or Primary Quantity) mass(??) M
, length L , time T , temperature(??)
3 Physical Quantities expressed by the Basic
Dimensions Examples 2. Dimensions
associated with Common Physical Quantities
(Table 1.1)
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1.2.1 System of Units
1./ Definition a particular way of attaching
a number to the quantitative dimension 2./
Representative Systems 1) SI Unit (International
System ?????) 2) British Gravitational(BG)
System(or English Unit ?? ?????) 3)
English Engineering(EE) System
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3. Examples 1) force 2) mass 3) energy(or
work) 3) power 4) temperature
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4. SI Prefixes (Table 1.2) 5. Value for
Gravity(?????) 1 Standard value 2
Variation from to 3
Nominal value 6. Significant Figures(????)
in general less than 3 7. Remarks The
centimeter is not an accepted unit of length in
the SI system, so for most problems in fluid
mechanics in which SI units are used, lengths
will be expressed in millimeters or meters.
20
1.3 Analysis of Fluid Behavior
8. Nine Fundamental Dimensions and Their Units
(see 1 p4 Table 1.1)
Fluid Mechanics Fluid Statics(?? ???)
Fluid Dynamics(?? ???)
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1.4 Measures of Fluid Mass and Weight
  • 1.4.1 Density(??)
  • the primary property used to determine if the
    continuum assumption is appropriate
  • 1 definition mass per
    unit volume
  • 2 density at standard atmospheric conditions
  • air , water
  • 3 Density of water as a function of temperature
    (p12 Fig. 1.1)
  • 4 Specific Volume(???)
    (1.5)
  • C. F. Standard Atmospheric Conditions (??????)
  • - refer to sea-level(???) conditions at
    latitude(??)
  • pressure at sea level
  • temperature

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1.4.2 Specific Weight (???) - weight per unit
volume
1.4.3 Specific Gravity (??) the
ratio of the density of a substance to that of
water at a reference(??) temperature of ,i.e.,
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Table B.2
27
Table B.4
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1.5 Ideal Gas Law
1. Definition of Ideal Gas(????) (Perfect Gas
????) fluid whose molecules have a mutual
effect arising solely from perfectly elastic
collision (i.e., neglecting intermolecular
forces) 2. Ideal Gas Law (or Perfect Gas Law,
Equation of State for an Ideal Gas) where
absolute pressure and absolute
temperature gas constant C. F,
It is known to closely approximate the behavior
of real gases under normal conditions when the
gases are not approaching liquefaction.
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3. Pressure in a Fluid at Rest 1 Definition
normal force per unit area exerted on a plane
surface(real or imaginary) immersed in a fluid
and is created by the bombardment of the surface
with fluid molecules 2 Dimension 3 Unit
4. Value of Gas Constant 1) where
universal gas constant
molar mass of gas 2) Extensively used Value
of of air
because for air
30
  • 5. Example 1.3
  • ltSolutiongt
  • ?
  • ?

31
1.6 Viscosity(??)
1./ Definition and Effect 1 Definition (origin
of viscosity) - microscopic transport process
the process of momentum transfer in the direction
of the velocity gradient (but opposite direction)
by the molecular motion - cohesion and molecular
momentum exchange between fluid layers -
internal stickiness of a fluid 2 Effect of
Viscosity - cause the fluid to adhere to the
surface no-slip condition (????) i.e. -
appear as shear stresses between the moving layers
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  • relates the local stresses in a moving fluid to
    the strain rate of the fluid element
  • 2. Newton's Viscosity Law (Fig. 1.2, 1.3)
  • 1 Application Range
  • - common linear fluid such as air, water, oil
    etc
  • - laminar flow(??)
  • 2 Law

  • where
  • shear stress(????)
  • dynamic viscosity coefficient(???????)
    (or absolute viscosity, viscosity)
    , constant proportionality(?? ??)
  • velocity gradient interpreted as
    a strain rate

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Solid
Fluid
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3. Newtonian Fluid(????) (Fig. 1.4) 1 Definition
- fluid of which the shear stress is
directly proportional to the velocity gradient 2
Examples air, water, oil 3 Non-Newtonian Fluid
(?????) - fluid which does not satisfy the
Newton's viscosity law - liquid plastics,
blood, slurries, toothpaste 4. Effect of
Temperature on the Fluid Viscosity 1 Liquid
Case 2 Gas Case (Fig.1.10)
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Newtonian Fluid
Non-Newtonian Fluid
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Note ! The percentage change of viscosity in a
liquid is much greater than in a gas for the same
temperature difference. 5. Kinematic Viscosity
Coefficient(?????)
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6. Example 1.5
  • ltSolutiongt
  • ?
  • ? (a)
  • ? (b)

39
1.7 Compressibility(???)
1.7.1 Bulk Modulus (or Bulk Modulus of
Elasticity ?? ????) 1. Meaning of
Compressibility the amount of change in
volume or density with the change in
pressure 2. Bulk Modulus of Elasticity
(??????) 1 Role a common way to describe the
compressibility of a fluid 2 Definition i.e.,
is defined as the ratio of the change in
pressure and relative change in density
while the temperature remains
constant
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3 Unit same as pressure 4 Value of at
standard condition - for water 2,100
(21,000 atm) - for air 1
atm - Note !(see Text p18) In general ,
for gas is equal to the pressure of the gas.
To cause a 1 change in density of water a
pressure of 21 (210 atm) is required thus
liquids are often assumed to be incompressible.
For gases, if significant changes in density
occur, say 4, they should be considered as
compressible for small density changes they may
also be treated as incompressible.
41
1.7.2 Compression and Expansion of Gases 1.
Relationship between pressure and density 1
Isothermal Process (????) 2 Isentropic
Process (????? ??) where 1.7.3 Speed
of Sound(??) 1. Definition see T p24 C.F.
Value of c of water at standard condition
1,450 m/s
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2. for ideal gas in isentropic process

3. Values of specific heat ratio
of air at various temperature see Table
B.3, B.4 Speed of sound in air at various
temperature see Table B.1, B.2 4.
Example 1.7
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Table 1.6
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1.8 Vapor Pressure (???)
1. Definition - pressure at which a liquid boils
and is in equilibrium with its own vapor -
pressure resulting from molecules in the gaseous
state 2. Relationship local absolute
pressure - vapor pressure of the liquid
1 if the only exchange between liquid and
vapor is evaporation(??) at the interface 2
if The vapor bubbles(??) begin to appear in
the liquid.(transition from the liquid state to
the gaseous state) ? Cavitation(????)
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3. Value of Vapor Pressure (Table B.2)
- The is different from one fluid to
another - The of water at SAC(??????)
is 1.70 absolute - The is highly
dependent on pressure and temperature, e. g.,
the of water increases to 101.3
if the temperature reaches 4.
Cavitation(????) 1 Definition the phenomena
appearing bubbles locally when 2 Cavitation
Number dimensionless parameter describing
flow-induced boiling where
characteristic flow velocity
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3 Critical Value of Depending on the
geometry, a given flow has a critical value of
below which the flow begin to cavitate. 4
Effect of Cavitation
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1.9 Surface Tension(????)
1. Meaning and Property 1 Meaning Surface
tension is a property that results from the
attractive forces(??) between molecules. 2
Property It manifests itself only in liquids.
see Text 3 Unit ,i.e., force per unit
length
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4 Force due to surface tension - results from
a length multiplied by the surface tension - the
length to use is the length of fluid in contact
with a solid, or the circumference in the case of
a bubble 2. Pressure inside the Droplet and
Bubble(see p19-20 and Fig.1.11) 1 Droplet(??
??) 2 Bubble(??) where sigma
surface tension 3. Capillary Tube(???)(see p27
Fig.1.8)
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