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Lecture Notes on Fluid Mechanics I 5th Ed. Update by B. R. Munson, D. F. Young, and T. H. Okiishi

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Lecture Notes on Fluid Mechanics I

5th Ed. Update

by B. R. Munson, D. F. Young, and T. H. Okiishi

메카트로닉스전공

유체역학 1 강의교재(2학기 과목)

http://www.mecha.ac.kr/down.php강의노트

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”

CH 1. Introduction

▣ Fluid Mechanics(流體力學) :

* 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 fluids[1]

* 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 magnitude[T]

- 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

- 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 + Gas[1]

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(凝集力) so as to maintain a relatively fixed volume

2) characteristics

- retain a definite volume in a container

- form a free surface(自由表面) in gravitational field(重力場)

- strong intermolecular cohesive force

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

- 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 gas=volume of container

- Gas cannot form a free surface, and thus gas flows rarely concerned with gravitational effects other than buoyancy(浮力).

- 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.

the spacing between molecules at a normal pressure and temperature = order of

- number of molecules per
- 3. Continuum(連續體)
- 1] Meaning
- 1) condition for macroscopic point of view :
- dimension of volume element >> 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]

- 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

Continuum Hypothesis

All substances are composed of an extremely large number of molecules. :

Molecules interact with each other via collision and intermolecular forces => ignore the molecular nature of matter and assume that the matter is continuous : Continuum hypothesis

1.2 Dimensions (次元), Dimensional Homogeneity (차원의 同次性), and Units (單位)

1. Dimension

1] Definition

: the measure by which a physical variable is expressed qualitatively ; length, mass

2] 4 Basic Dimensions(or Primary Quantity)

mass(質量) [M] , length [L] , time [T] , temperature(溫度) [ ]

3] Physical Quantities expressed by the Basic Dimensions

Examples :

2. Dimensions associated with Common Physical Quantities

(Table 1.1)

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 : 國際單位系)

2) British Gravitational(BG) System(or English Unit ; 영국 중력단위계)

3) English Engineering(EE) System

5. Value for Gravity(重力加速度)

1] Standard value :

2] Variation : from to

3] Nominal value :

6. Significant Figures(有效數字) : 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.

1.3 Analysis of Fluid Behavior

8. Nine Fundamental Dimensions and Their Units

(see [1] p4 Table 1.1)

Fluid Mechanics

= Fluid Statics(유체 정역학) + Fluid Dynamics(유체 동역학)

1.4 Measures of Fluid Mass and Weight

- 1.4.1 Density(密度) :
- 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(比體積) (1.5)
- C. F. Standard Atmospheric Conditions (標準大氣條件) ;
- - refer to sea-level(해수면) conditions at latitude(緯度)
- pressure at sea level =
- temperature=

- weight per unit volume :

1.4.3 Specific Gravity (比重)

= the ratio of the density of a substance to that of water at a reference(基準) temperature of

,i.e.,

1.5 Ideal Gas Law

1. Definition of Ideal Gas(理想기체) (=Perfect Gas ; 完全氣體)

: 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.

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 ;

- <Solution>
- ◈
- ◈

1.6 Viscosity(粘性)

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 (粘着條件)

i.e.

- appear as shear stresses between the moving layers

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(層流)
- 2] Law
- where
- : shear stress(剪斷應力)
- : dynamic viscosity coefficient(역학적점성계수) (or absolute viscosity, viscosity) , constant proportionality(비례 상수)
- : velocity gradient interpreted asa strain rate

Fluid

3. Newtonian Fluid(뉴톤유체) (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 (非뉴톤유체);

- 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)

Non-Newtonian Fluid

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(動粘性係數)

- <Solution>
- ♠
- ♠(a)
- ♠ (b)

1.7 Compressibility(壓縮性)

1.7.1 Bulk Modulus (or Bulk Modulus of Elasticity ; 체적 탄성계수)

1. Meaning of Compressibility

: the amount of change in volume or density

with the change in pressure

2. Bulk Modulus of Elasticity (體積彈性係數)

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

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.

1.7.2 Compression and Expansion of Gases

1. Relationship between pressure and density

1] Isothermal Process (等溫過程) ;

2] Isentropic Process (등엔트로피 과정) ;

where

1.7.3 Speed of Sound(音速)

1. Definition ; see [T] p24

C.F. : Value of c of water at standard condition : 1,450 m/s

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

1.8 Vapor Pressure (蒸氣壓)

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(蒸發) at the interface

2] if

The vapor bubbles(氣泡) begin to appear in the liquid.(=transition from the liquid state to the gaseous state) Cavitation(空洞現象)

3. Value of Vapor Pressure (Table B.2)

- The is different from one fluid to another

- The of water at SAC(표준대기상태) 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(空洞現象)

1] Definition

: the phenomena appearing bubbles locally when

2] Cavitation Number

: dimensionless parameter describing flow-induced boiling

where : characteristic flow velocity

: Depending on the geometry, a given flow has a critical value of below which the flow begin to cavitate.

4] Effect of Cavitation

1.9 Surface Tension(表面張力)

1. Meaning and Property

1] Meaning : Surface tension is a property that results from the attractive forces(引力) between molecules.

2] Property

* It manifests itself only in liquids.

* see Text :

3] Unit :

,i.e., force per unit length

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(작은 방울)

2] Bubble(氣泡)

where sigma ; surface tension

3. Capillary Tube(毛細管)(see p27 Fig.1.8)

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