Fluid Mechanics (Week 1) Engineering Mechanics Fluid Mechanics (Week 1) Chapter 1Introduction Hsin-Yuan Miao, Ph. D. Assistant Professor Department of Mechanical Engineering National Kaohsiung University of Applied Science 415 Chien-Kung Road, Kaohsiung, 80778, Taiwan R. O. C. TEL : 886-7-381-4526 ext. 5351 FAX : 886-7-3831373 Mobile : 886-937-215-638 E-MAIL : kenymiao@cc.kuas.edu.tw http://www2.kuas.edu.tw/prof/kenymiao/index.html

What is “Fluid”?(water, oil, air)(contiuum連體) Chapter 1: Introduction ---1.1 Some Characteristics of Fluids What is “Fluid”?(water, oil, air)(contiuum連體) ------is based on how materials deform under the action of an external load. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude.(flow). A shearing stress is created whenever a tangential force acts on a surface When common solids such as steel or other metals are acted on by a shearing stress, they will initially deform (usually a very small deformation), but they will not continuously deform (flow). What is “rheology”(流變學)?(slurries, tar, putty, toothpaste)

Shearing Stress

Primary quantities---lenth(L), time(T), mass(M), temperature(θ) Chapter 1: Introduction ---1.2 Dimensions, Dimensional Homogeneity, and Units A system for describing these characteristics both qualitatively (定性)and quantitatively (定量). The qualitative aspect serves to identify the nature, or type, of the characteristics (such as length, time, stress, and velocity) The quantitative aspect provide a numerical measure of the characteristics.(units) Primary quantities---lenth(L), time(T), mass(M), temperature(θ) Secondary quantities---area=L2, velocity=LT-1, density=ML-3, F=MLT-2, σ=FL-2=ML-1T-2 And see page 3, Table 1.1

Dimensionally homogeneous (因次均一性) 方程式的各項應具有相同的因次 1。For example of Velocity V = V0 + at LT-1 = LT-1 + LT-1 2。For example of gravity D = 16.1t2 ------ constant=LT-2 » D = ½ g t2 ------g = 32.2 ft/s2, 9.8 m/s2 。restricted homogeneous ? 。general homogeneous ? 1.2.1 System of Units – BG, SI

1.3 Classification of Fluid Flow 1 Viscous versus Inviscid Chapter 1: Introduction ---1.3 Analysis of Fluid Behavior 1.3 Classification of Fluid Flow 1 Viscous versus Inviscid 2. Internal versus External 3. Compressible versus Incompressible 4. Laminar versus Turbulent 5. Natural (unforced) versus Forced 6. Steady versus Unsteady 7. One-, Two-, Three-Dim.

1.4.1 Density 密度 (sluds/ft3, kg/m3) Chapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight 1.41 Density 密度 1.42 Specific weight 比重量 1.43 Specific gravity 比重 1.4.1 Density 密度 (sluds/ft3, kg/m3) = ρ (rho) =is defined as its mass per unit volume. = used to characterize the mass of a fluid system. = 不同流體，其值變化極大 = 但對單一流體，隨壓力與溫度之變化極小(氣則不然)

Figure 1.1 Density of water as a function of temperature Chapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight Figure 1.1 Density of water as a function of temperature

1.4.2 Specifics Weight (lb/ft3, N/m3)(比重量) Chapter 1: Introduction ---1.4 Measure of Fluid Mass and Weight 1.4.2 Specifics Weight (lb/ft3, N/m3)(比重量) = γ (gamma) = is defined as its weight per unit volume. = is related to density through the equation γ= ρg = is used to characterize the weight of the system. 1.4.3 Specific Gravity(沒單位) = SG = is defined as the ratio of the density of the fluid to the density of water at some specified temperature. = SG = ρ/ ρH2O 4ºC ρHg = (13.55)(1.94 slugs/ft3) = 26.3 slugs/ft3 ρHg = (13.55)(1000 kg/m3) = 13.6x103 kg/m3 Hg 20 ºC SG= 13.55

P = ρRT Ideal Gas Law(近液化狀態時不合用) Chapter 1: Introduction ---1.5 Ideal Gas Law Gas are highly compressible in comparison to liquid. 氣體密度的改變直接引起壓力和密度的變化。 P = ρRT Ideal Gas Law(近液化狀態時不合用) 只要不要接近液化狀況，在正常狀態下的氣體，其行為可以此方程描述 P = absolute pressure 絕對壓力 ρ = the density 密度 R = a gas constant氣体常數(視氣体種類及分子量而定) T = the absolute temperature 絕對溫度

絕對壓力 = 錶壓力 + 大氣壓力(靜壓) 相對於 Gage pressure 單位： Chapter 1: Introduction ---1.5 Ideal Gas Law 絕對壓力 = 錶壓力 + 大氣壓力(靜壓) 相對於 Gage pressure 單位： BG： lb/ft2 (psf), lb/in2 (psi) SI： N/m2 (Pa) 例：大氣壓14.696 psi, 101.33 kpa 14.7 psi, 101.33 kpa For example.. 胎壓 = 30 psi 絕對壓力 = 30 + 14.7 = 44.7 psi

Figure 1.2 Behaviour of a fluid placed between two parallel plates Chapter 1: Introduction ---1.6 Viscosity 1.6 Viscosity (黏度) ρ與γ(流體”重”的量測)不足以描述流体的不同（流動性之不同）！例如：水與油！故須另一個參數可用來描述”流動性” 例：以實驗 速度梯度 u=f(y)=U*(y/b) Figure 1.2 Behaviour of a fluid placed between two parallel plates

1。在圖1。2中速度梯度=定值，但一般流体會複雜許多。 Chapter 1: Introduction ---1.6 Viscosity 1。在圖1。2中速度梯度=定值，但一般流体會複雜許多。 2。流体”黏著”在固體邊界乃為體力學的一項重要發明。稱為”無滑動情況”(no-slip condition)。(氣、液皆然) • γ 剪力 τ = P/A 剪應變 = ? 在時間小增量бt，AB有個бβ, 而tan бβ≈ бβ=бa/b，但бa=Uбt 所以 бβ=Uбt/b (是P與t的函數) • γ • γ 故將бβ微分得 = lim бβ/ бt = U/b=du/dy бt---0 • γ • γ 知τ正比於 τ ≈ 定τ = μ du/dy 此μ為絕對黏度 absolute viscosity

牛頓流體 μ = 絕對黏度 = 動力黏度(dynamic viscosity) =黏度(為斜率且呈線性) 受流體種類而定，且受溫度影響 Chapter 1: Introduction ---1.6 Viscosity μ = 絕對黏度 = 動力黏度(dynamic viscosity) =黏度(為斜率且呈線性) 受流體種類而定，且受溫度影響 牛頓流體 Figure 1.3 Linear variation of shearing stress with rate of shearing strain for common fluids

非牛頓流體 =剪力與剪應變不呈線性。例v-1.4 Chapter 1: Introduction ---1.6 Viscosity 非牛頓流體 =剪力與剪應變不呈線性。例v-1.4 μ = FTL-2 = lb/ft2 = N*s/m2 流體的黏度變化大 受壓力影響不顯著，而溫度則非常大 在流體流動的問題中，ν(nu) = μ/ρ，(運動黏度)(L2/T, ft2/s, m2/s)

容積模數值越大，表示流体相對地不可壓縮-----施加的壓力很大，但dv卻很小。 Chapter 1: Introduction ---1.7 Compressibility of Fluid (用來區分可壓縮性) 1.7.1 Bulk Modulus(容積模數, 彈性模數) 1。某種已知質量的流體 ，當壓力改變時，流體的容積、密度，是否改變? 2。流體可被壓縮? dp = 微小壓力差 v = 體積，dv =體積的微小改變量 Eυ = - dp/ (dv/v) 壓力的增加，体積的減少 因為 m = ρ v, 若v ，則 ρ Eυ = dp/ (dρ/ρ) FL-2, lb/in2(psi), N/m2(Pa) 容積模數值越大，表示流体相對地不可壓縮-----施加的壓力很大，但dv卻很小。 在 故不可壓縮(incompressible)(液體) (液體之容積模數值在被壓縮時會增大)

1.7.2 Compression and Expansion of Gas 1。當氣體被壓縮(或膨脹)時，壓力與密度的關係依過程而定。 2。若在等溫，則是等溫過程(isothermal process), 由PV=NRT知 p/ρ=常數。 3。若壓縮(或膨脹)時無摩擦，且與外界無熱交換，則為等熵過程(isentropic process), p/ ρk=常數。(k=cp/cv).(cp:定壓比熱，cv:定容比熱) 1.7.3 Speed of Sound 1。流體壓縮性的另一個重要的結果，係將擾動源導入流體中某一 點而產生有限的速度。 2。在管流中，閥門突然關上，擾動上傳呈聲速 =c。 3。在流體中c的大小與壓力、密度的改變有關。 C = √ (dp/dρ) = √ (Ev/ρ) 等熵 則 c= √ kRT

1.8 Vapor Pressure 蒸氣壓受溫度影響。 沸騰(boiling)為流體中蒸汽泡的形成現象，起因於流體 的絕對壓力達到蒸汽壓力。 流体流動時會形成較低的壓力，當壓力低至蒸汽壓力時便產生沸騰。 孔蝕(cavitation)

1.9 Surface Tension γπR2h=2πRσcosθ h = 2σ cosθ/γπR Chapter 1: Introduction 1.9 Surface Tension γπR2h=2πRσcosθ h = 2σ cosθ/γπR Figure 1.4 Effect of capillary action in small tubes. (a) Rise of column for a liquid that wets the tube. (b) Free-body diagram for calculating column height. © Depression of column for a nonwetting liquid