Fluid Mechanics
School of Mechanical Engineering
Yeungnam University
비행원리: Can you fly?
Chapter 1. Introduction
Fluid Mechanics in Engineering Fluids/Continuum Hypothesis Fluid Primary Properties Secondary Properties Dimension and Units Scope of Fluid Mechanics Methodology
Fluid Mechanics in Engineering
Newton’s 2nd Law:
Fluid / Flow: substance/motion, matters
Engineering: Application of Basic Laws
Fluid transport( 유체수송 ): pumps, compressors
water supply, oil, gas pipelines
Energy generation( 에너지 발생원 ): steam turbines
engines, hydroplant
Environmental Control( 대기순환 제어 )Transportation( 운송체 역학 ): airplane, car, ship
Bio-fluid mechanics( 인체유동 ): lung, cardio-vascular
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Definition of Fluids(1)
*A fluid is a substance that deforms continuously under the action of an applied shear force or stress.
*The process of continuous deformation is called Flowing.
*A fluid is a substance that can resist shear only when moving.: the relation between stress and the time rate of deformation
Response of solid and fluid to applied shear force (a) instant of application(b) to a short time later, (c) to a later time
solid
fluid
Definition of Fluids (2)
Phase gas rarefied gas cohesive force liquified gas fluid liquid: keeps volume solidConsequence of molecular spacing and intermolecular forces
cf. rarefied gas; 지구의 대기권과 외기권의 경계층에서 분포 liquified gas; 액화연료
Fluid is one of continuum materials; cf. gas, liquid, solid; continua
Continuum. Hypothesis Even in a point volume, there are extremely large numbers of fluid individual molecules. To ignore molecular nature of matter, a point volume has the bulk property established by infinite number of molecules, called ‘fluid property.’
cf. molecular dynamics establishes properties(물성치 )
cf. a volume of in air has molecules
At very high altitude , the continuum model is invalid.
Continuum Hypothesis ( 연속체 가설 )
109
mm3 7103
PROPERTIES-density(1)
Density: depends on the size and locations of the chosen volume
mass per unit volume
water : air : mercury:
V
m
3/1000 mkg3/25.1 mkg
3/500,13 mkg
Practicalmeasureddensity
VNature ofmolecules
V
Statisticalbehavior
Size of Point Volume
PROPERTIES-density(2)
Definition of continuum fluid density
incompressible: density variation may be neglected
: point fluid concept.
Specific volume : ( 비체적 ) Specific weight : ( 비중량 ) Specific gravity : ( 비중 )
V
m
VV
lim
1
v
g
ref
S
The reference fluid is pure water at 4 deg. C and 101,330 Pa, 1000 kg/m3.
Shock formation in front of F-18 flight at Mach=1.4, altitude=35,000 ft
Supersonic wind tunnel testing
Density Difference : Schlieren Photo
PROPERTIES-pressure(1)
Pressure
•the normal compressive force per unit area on real or imaginary surface in the fluid. ( 단위면적당 수직압축력 )
•units; Pa(pascal) Psi
•101,325 Pa = 1 atm, 14.7 psi = 1 atm•acts a role to distribute energy homogeneously.•Differences of pressure are more important than levels of pressure
A
FN
AA
lim
2/ mN2/ inlb f
outin ppp
PROPERTIES-pressure(2)
Ambient ( 영국 공학계 , 14.7 psia)pressure ( 101,330pa)
Absolutepressure
Gage pressure
Vacuum pressure
psia=pounds per square inch,absolutepsig=pounds per square inch, gagepa : 2/1 mN
Absolute pressure= Gage Pressure( 계기압 ) + Ambient Pressure( 계기주위압 )
Vacuum pressure= Ambient Pressure - Absolute Pressure
( 진공압 ) = - Gage Pressure
PROPERTIES-thermal behaviors(1)
Thermal behaviors 1. compressible fluid (air, gases): 압축성유체
dependent on thermal properties; T, h, e, …
: specific enthalpy
: specific heats
2. incompressible fluid (water, liquid): ignored, 비압축성유체
Specification of only two of the properties allows us to determine values of the other properties.
Equation of State
( 상태방정식 )
pvup
uh
pvv T
hCT
up
c ))
cc vp
),...,(),,( phhpTT
Ideal Gas approximation: gases at the surroundings in low pressure and high temperature.
: equation of state ( 상태방정식 )
R: Gas constant
In general, the air is considered as an ideal gas.There also exist state equations of liquid and solid. For most practical purposes, we treat liquids as incompressibleFluids.
RTp
PROPERTIES-thermal behaviors(2)
KkgmNWMweightmolecular
RR ./.
..
83140
,/287 kgKJM air molekgkgMW /
Viscosity ( 점도 )•Definition; from the microscopic nature in molecular motion
characterized by v × l v ; average velocity of a moleculel ; mean free path or, characteristic length ( 평균자유경로 )
molecular kinematics continuum motion
Transport properties: viscosity (momentum), conductivity (heat, energy), diffusivity (mass)
PROPERTIES-viscosity(1)
For a fluid particle moving shear stress is important when moving only, shear stress ~ shear strain rate or rate of deformation
e
yy
uu
u
tydy
dute urel
ydy
duuy
dy
duuurel
)(when
vl
LawsNewtondy
duor
dy
du
ratestraindy
du
t
tdy
du
y
e
tsmallforsmall
:
':~
:
)tan(
:
The coefficient is the viscosity.
t=0 t=t
y
Shear deformation rate ( 전단변형율 )
The coefficient called “viscosity” which describes the stiffness of substance.
• dimension; or,• units; kg/(m.s) or Pa.s or stokes• Kinematic viscosity:
•Newtonian Fluid: obeys 뉴턴유체
]/[ 2LFt ]/[ LtM
PROPERTIES-viscosity(3)
yu
)/( 2 scm
Shear thinning
Shear thickening
•Two main reasons to produce the viscosity• attraction force between molecules• momentum change of molecules
•temperature dependency: as temperature increases, gas viscosity increases / liquid viscosity decreases .
liquid
gas
He, H
Viscosity
Illustative problems:
1) viscous force over a liquid film
2) torque of a rotating disk over a thin film
SECONDARY PROPERTIES- bulk modulus, E
*Bulk modulus of elasticity ( 체적탄성계수 ), E is similar to Young’s modulus. ;degree of compressibility
same unit as pressure
normal force
liquid volume strain volume dV/V V
29 /101.2:
dv
dp-v
/
mNwater
d
dpdv
dpv
vdv
dpE
SECONDARY PROPERTIES -thermal expansion coefficient,
Coefficient of thermal expansion, ( 열확장계수 ) ;expand as temperature increases
13
14
105.3:
][105.1:
11
1/
K해수면공기Kwater
dT
d
dT
dv
v
dT
dv
vdT
vdv
T
T
T
T
Surface Tension. -- forces at interfaces between gas - liquid, liquid-liquid and liquid - solid. -- a liquid, being unable to expand freely, will form an interface with a second liquid or gas.
Definition of surface tension force; cf. Units; N/m ( tension force per unit length )
Illustrative problem: an arbitrary curbed plate
.: forcesappliedFl
1R2R
1L
2L 1L 1L
2L
2R
SECONDARY PROPERTIES- surface tension,
1 1R1
1L
2L 2L
12 sinL
21
21
2122
21
211
12
222
11121
22112112
)11
()sin2
sin2
sin2
sin2(
sin2
sin2.0
sin2sin2sin2sin2
RR
RpRor
RRLR
L
LR
Lp
LR
LRas
RRpLL
Illustrative problems; cylinder, hemi-sphere
SECONDARY PROPERTIES- surface tension(2)
Surface tension force = pressure force
SECONDARY PROPERTIES- surface tension(3)
Because of the surface tension, the fluid interface area tends to become minimum.
Capillary Tube
gRh
hRgR
cos2
cos2 2
SECONDARY PROPERTIES- capillary
Upward tension force= weightof water column
vpp
22/1 v
ppC va
a
Cavitation -- at local pressure, (vapor pressure) vaporization takes place instantly, and as soon as the pressure recovers, it dies out. -- cause impact on surface and makes damage.
: cavitation number
SECONDARY PROPERTIES- cavitation
DIMENSION AND UNITS OF FLUID SYSTEM
SCOPE OF FLUID MECHANICS
METHODOLOGY FOR ANALYSIS
Problem solving steps
Theoretical method ( 이론적 방법 )
Experimental method ( 실험적 방법 ) Computational method ( 전산적방법 )
computational experiment experimental computation