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破久箱邢
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流 - 流量 - 流度數力 - 流力類立 1-1 - 1 - 流 Fluid 流 Flow (Solid) --- 狀

(Solid) (Liquid) (Gas) 1-3 1-4 若力來流力行流流流 (Fluid element) 度 0 o C 狀

1 流 - 流量 - 流度數力 - 流力類立流 Fluid 流 Flow (Solid) --- 狀 (Liquid) --- 狀流 Fluid (Gas) --- 狀流流流 Flow 流 (Fluid) 流 (Flow) 流流 (Solid) (Liquid) (Gas) 若力來流力行流流流 (Fluid element) 度 0 o C 狀 1 cm 3.5x10 19 度 10-6 cm 流 1 cm x 1 cm x 1 cm 流流 (Fluid element) 流度 1 cm 流度

2 連 (Continuum Hpothesis) 力力 xial force 力力力 (Shear force) 力流力不流行流力流力流流度度流連 (Continuum) 力 (Moment) (Torsion) 量流力力 (Shear force) 行力力力 (Shear stress) 力 x F F τ = θ F 力力流力連 1-9 x (Strain) θ = 量 θ 1 x x 1 u 率 (rate of strain) = = = 度度 t t t 量度率 1-10 度度 (Velocit gradient) F x 流力流 θ 流 du d 流 u 率率 1-11 力 x τ θ = 流率 ( 度度 ) 力 θ du τ t = d 律 1-1

3 流度度力流 (Dimension) (Unit) 理量度度力度 [L/T][m/s] [km/hr] [mile/hr] (Dimension) τ τ 流力率度度 du/d 1-13 度 [L] [T] 量 [M] 力量 [F] 度 [Θ] F = m a [F] = [MLT - ] 1-14 (Dimension uniformit) 量 [M] Kg, g Slug, lbm 理度 [L] m, cm ft, in x(t) = x o + vt a t 量, 力 [T] [F] hr, sec N, Kgf sec lbf L L [ L] = [ L] + [ T ] + [ ] T T T 度 [Θ] C, K F 流理流理力度流 1. (Extensive propert) 流量理量量量力量. (Intensive propert) 量流理量度度數度力流理力 (Pressure) 度 (Densit) (Specific Weight) (Specific Gravit) 數 (Viscosit) 力 (Surface Tension) (Specific Heat) 數 (Bulk modulus) (Vapor pressure)

4 1. 力 (Pressure) 力力 (Normal force) F P = F 力力力力 (Compressive stress)[f L ] F 力 1-19 見力 (SI) 1.0 N/m = 1.0 Pa Pascal = 0.01 mbarmillibar mb = 0.01 hpa 1.0 kpa = 1000 Pa = 1000 N/m 1.0 psi = 1.0 lbf/in pound per square inch = 144 psf pound per square ft, lbf/ft Blaise Pascal ( ) 1-0 見力. 度 (Densit) 1 力 1 atm = N/m = kpa = 1013 mbar = 760 mm-hg = 14.6 psi 力 h 度流量流量 ρ = 流度 [M/L 3 ] 流度度力力狀便度. 度 (Densit) 1000 度狀 Densit (kg/m 3 ) Temperature (C) 度力度 4 o C 狀度 1000 kg/m PV p 力 T 度 ( o K = o C + 73) n 數 R u = 8.05 cm 3 -atm-g/ o K/mol = J/ o K/mol 數狀 nm R P = u T V M M 量度 nm V = nr T = ρ u 1-4 4

. 度 (Densit) 狀 P = ρrt 數 R = R u /M 類不不數 R = 87 J/ o K/kg 數 R = 461 J/ o K/kg 不數 R u = 8.05 cm 3 -atm-g/ o K/mol = 8.314 J/ o K/mol 度度力度 1-5 Gas Constant of Water Vapor R R = M u w 1 1 1 8.

5 . 度 (Densit) 狀 P = ρrt 數 R = R u /M 類不不數 R = 87 J/ o K/kg 數 R = 461 J/ o K/kg 不數 R u = 8.05 cm 3 -atm-g/ o K/mol = J/ o K/mol 度度力度 1-5 Gas Constant of Water Vapor R R = M u w J K mol R = 18 g mol 1 1 R = 461 J K kg H O H Molecular Weight (M w ) Hdrogen = 1.0 g mol -1 Oxgen = 16 g mol -1 Water = 18 g mol 度 (Densit) 3. (Specific weight) 流量流量 γ = 流 [F L 3 ] 量量力度 g (= 9.81 m/s ) γ = ρg γ water = 9810 N/m (Specific gravit) 流度 γ ρ S = = γ ρ water water γ 流 γ water = 9810 N/m 3 度力度 4 o C 狀參數 S = 13.6 度 (Densit)(Specific weight) (Specific gravit) 例 (0 o C) 度 P atm = x 10 3 N/m 度 T = 0 o C = o K 度 P ρ = RT 101,300 N / m = = 1.0 kg / m o o 87 J / K / kg K γ = ρg = 1.0 kg / m 9.81 m / s = N / m air air N / m S = ρ γ ρ = γ = 9810 N/ m = water water

6 5. 度 (Concentration) 度流量量 Conc. = 流度 [M/L 3 ] 1.0g 1.0 若略度 1.0 g/liter = 1.0 kg/m 3 5. 度 (Concentration) 度量量量 Conc. = 流量度 1.0 mg 1(=1.0 kg) 量量 1.0 ppm (= part per million = 10-6 ) 度 1.0 ppm = 1.0 mg/kg = 1.0 mg/liter1.0 ppb (= part per billion = 10-9 ) = 1.0 µg/kg = 1.0 µg/liter 度 (Concentration) (Greenhouse Gases) 度量 Conc. = 流度度 360 ppm 度 0.19 ppm (= 190 ppb) 數 (Viscosit) 兩行流數流力流易度流數量流數量流易 d F du 流流率 ( 度度 ) 力 du τ = µ 律 d 律 µ 流力數 [F T/L ]

數 (Viscosit) 數流流力流流數流力流數力流 Joule s experiment 流 1-37 1-38 數 (Viscosit) Greek Smbols 力數 (Dnamic viscosit) du τ = µ d F F T L / T = L L L 律 (Newton s viscosit law) µ 流力數 [F T/L ] 數

7 數 (Viscosit) 數流流力流流數流力流數力流 Joule s experiment 流數 (Viscosit) Greek Smbols 力數 (Dnamic viscosit) du τ = µ d F F T L / T = L L L 律 (Newton s viscosit law) µ 流力數 [F T/L ] 數 (Kinematic viscosit) µ ν = ρ 數 [L /T] µ = ρ ν 數 (Viscosit) du τ = µ d 流 (Newtonian fluid) 流率 ( 度度 ) 力數數見流流論流流力 τ 流流流 (Non-Newtonian fluid) 流數力數流率力糖 µ 率 ( 度度 ) du d 流流力率

Newtonian vs. Non-Newtonian Toothpaste Paint Water 例滑力兩流若不 U 滑力數 0.

0 mm 流流度不滑 No slip 1-43 1-44 x U = 10 cm/s d = 5.0 mm τ = 0.1 m / s 0.

005 m 力 N / m = 0 流度 u = 0 = d 流度 u = U 流 u () = U d 力 du τ = µ d = d U = µ

8 Newtonian vs. Non-Newtonian Toothpaste Paint Water 例滑力兩流若不 U 滑力數 Ns/m 力 U = 10 cm/s Corn Starch x d = 5.0 mm 流流度不滑 No slip x U = 10 cm/s d = 5.0 mm τ = 0.1 m / s N s / m = m 力 N / m = 0 流度 u = 0 = d 流度 u = U 流 u () = U d 力 du τ = µ d = d U = µ d F D = τ 流不流力流力流流力 U = 10 cm/s d = 5.0 mm 力 du U τ=µ =µ d d = x 力 (Surface Tension) 力 (Surface Tension) 流力度力力 [F/L] 力流類度力 360 度力力 0 力不拉力

9 7. 力 (Surface Tension) (Capillar Tube) 力度度略力 θ h h θ πdσ 力拉 (Water Strider) 1-49 γ h(πd /4) π d ( σπd) cosθ = h γ 4 4σ cosθ h = γ d d 度 1-50 σ (Bubble) r 力 P i 力 P e 力 ( P P ) r π r σ = π i e P i πrσ P e 8. (Specific Heat) 1.0 kg 1.0 C (1.0 K) 量量 (Joule)(cal) (Kcal) 度不易度易度 15 C1000 cal/kg/ C = 4184 J/kg/ C 880 J/kg/ C r 力 ( P P ) i e σ = r 陸 (Land/Sea Breeze) 9. 數 (Bulk modulus) 流 (Compressibilit) 數 E V P = V / V P 流力量 V 流量 V / V 率數 [F/L ] 力陸 P 1 P 陸輻度度量度度 1-53 Gas V 1 Gas V

10 9. 數 (Bulk modulus) 10. (Vapor pressure) 數流力更流不易數 E v =.19x10 9 Pa 1.0 % 力 16 力不流 (Incompressible Fluid) 狀數 E v = 1.013x10 5 Pa 1.0% 力 0.01 力易流 (Compressible Fluid) 1-55 若量 (vaporize) 若離力不便狀力便 (Saturation Vapor Pressure) 度量易度 Dnamic equilibrium (Vapor pressure) 10. (Vapor pressure) liquid 力 (Pa) 度 ( C) 便 (Water Vapor) 量度度 100% 1 力 100 o C 度 100 o C kpa 力不 100 o C 度 100 C 101 kpa 力 (Cavitation) 流力類流力 (Hdrostatics) 流狀力行流力 (Hdrodnamics) 流力行力 (Hdraulics) 流力行流力流輪葉 (Hdrolog) 利

11 流力類力 (erodnamics) 力行流力 (Environmental Fluid Mechanics) 流力行流力 (Geophsical Fluid Dnamics) 流力行流力類流力 (Magneto-hdrodnamics) 流力行 (Liquid Crstal) (Plasma) 流力 (Bio-Fluid Mechanics) 流力流力 (Bio-Fluid Mechanics) MIT 理論 (naltic Solution) 理論流理論.(Field Measurement) 量量量利 P V P 1 + z + = + z 1 γ g γ 1 + V g

12 3. 數 (Numerical Simulation) 數流流 4. (Laborator Experiment) 流 1-67 洞 1-68 n Questions? Suggested exercises: 1.5, 1.7, 1.11,

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