Fluid Mechanics School of Mechanical Engineering Yeungnam University

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

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 solid Consequence 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 )

PROPERTIES-density(1)  Density: depends on the size and locations of the chosen volume mass per unit volume water : air : mercury: Practical measured density Nature of molecules Statistical behavior 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 ) 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 수직압축 력 ) 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

PROPERTIES-pressure(2) Ambient ( 영국 공학계, 14.7 psia) pressure ( 101,330pa) Absolute pressure Gage pressure Vacuum pressure psia=pounds per square inch,absolute psig=pounds per square inch, gage pa : Absolute pressure= Gage Pressure( 계기압 ) + Ambient Pressure( 계기 주위압 ) 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, 비압축성 유체 Specification of only two of the properties allows us to determine values of the other properties. Equation of State ( 상태방정식 )

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 incompressible Fluids. PROPERTIES-thermal behaviors(2)

 Viscosity ( 점도 ) Definition; from the microscopic nature in molecular motion characterized by v × l v ; average velocity of a molecule l ; 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 u when The coefficient is the viscosity. t=0 t=  t y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 PROPERTIES-viscosity(3) 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

SECONDARY PROPERTIES -thermal expansion coefficient, Coefficient of thermal expansion, ( 열확장계수 ) ;expand as temperature increases

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 SECONDARY PROPERTIES- surface tension,

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 SECONDARY PROPERTIES- capillary Upward tension force= weight of water column

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