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

amF

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