5. Energy Equation. 1. Ideal fluid ( 理想流體 ):Ideal fluid is a fluid assumed to be "inviscid" (non-viscous fluid) 非黏性流體. Mathematically: µ = 0

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1 5. ner qation. Ieal fli 理想流體 :Ieal fli i a fli ame to be "inici" non-ico fli 非黏性流體為何要假設為理想流體? Mathematicall: µ 0 An: 假設為理想流體即表示流體粒子間, 或流體與邊界間無黏滯力作用, 故所有加諸在流體上之力, 均用以產生加速度, 無需克服阻力. Ditinction beteen ario fli an flo 各種流體與流況之區別 : Netonian fli τ Non-Netonian fli Incompreible fli Compreible fli µ ρ cont. Stea flo 0 t Untea flo Irrotational flo Ω 0 Rotational flo Ieal fli Inici fli, Non-ico fli µ 0 Real fli ici fli, ico fli Laminar flo 層流 rblent flo 亂流 3. -D ler' qn. alon the treamline

2 因為是 Inici fli µ 0 No ico force 無需考慮黏滯剪應力 τ 所受到的力 :rere,grait rere force: A A A Grait force: W ρ A Streamline ir.: W in θ ρ A F F m ma A A ρ ρ A a Recall Chap.3 ρ A A ρ A ρ A ρ ρ ρ 0 or 0 ρ -D ler' eqn. alon the treamline For Incompreible fli: ρ cont. ρ 0 4. Bernolli' qn. alon the Streamline Interatin -D ler' eqn. alon the treamline contant H Bernolli' eqn. alon the treamline

3 Amption 適用條件 :µ 0 Inici fli 理想流體 ρ cont. Incompreible fli Alon the treamline -D tea flo Bernolli eqn. i a efl relationhip beteen,,an. here H otal hea 總水頭 prere hea 壓力水頭 eleation hea 高度水頭 elocit hea 速度水頭 5. ner line L an Hralic Grae line HGL ner line L otal hea line 可用 Stanation be 量測總和之連線 Hralic rae line HGL ieometric hea line 可用 ieometer 量測總和之連線稱為 pieometric hea or hralic hea 3

4 4 6. Work-ner qation Mechanical ork-ener principle: Heat tranfer an internal ener are nelecte. W here W the ork one on a fli tem the chane in.. an K.. of a fli tem t t W For tea flo an incompreible fli: c.. A e t ρ here m m m m e.. A A A t c ρ ρ ρ

5 5 t W :o part Srface force: <i> Normal: prere <ii> Shear: friction.. A A F oer pa t W c Mechine ork: rbine t W mp t W Where ener etracte b trbine per nit eiht of fli ener ae b pmp per nit eiht of fli t t W Work-ner qation oer: hp lb ft 550 or U.S. nit kw J 000 or SI nit

6 7. 3-D ler' qation p p p p p p p p p p p p Withot icoit No hear Onl rere normal tre an rait bo force F F F We kno: ρ ρ a t a t ρ D Dt D Dt a D t Dt F ma ρ a F ma a ρa ρ t F ma ρ a ρa ρ t 6

7 F ma a ρ ρ ρ a ρ ρ t 整理如下 : ρa D ρ ρ Dt ρa D ρ ρ Dt ρa D ρ ρ ρ Dt 如令 i$ $ j k$ 則 0, D 故 ler' qn. 通式 ρ Dt ρ qn. of Motion or Momentm eqn. for ieal an incompreible fli can loe 4 nknon: b 3 eqn. of motion 方向 an continit eqn Bernolli' qn. in flofiel Interatin ler' eqn. for incompreible fli an tea flo p ρ p ρ p ρ ρ 7

8 8 ρ [ ] Ω Ω Ω Interation: [ ] H Ω Ω Ω Bernolli' eqn. an to point in flofiel ali for µ 0 ler' eqn. ρ cont tea flo irrotational 0 Ω

9 If rotational,onl ali hen 0 treamline fnction Bernolli' eqn. onl ali alon treamline in rotational flo. 9

10 5. ner qation. Ieal fli 理想流體 : Ieal fli i a fli ame to be "inici" non-ico fli 非黏性流體為何要假設為理想流體? Mathematicall: 0 An: 假設為理想流體即表示流體粒子間, 或流體與邊界間無黏滯力作用, 故所有加諸在流體上之力, 均用以產生加速度, 無需克服阻力. Ditinction beteen ario fli an flo 各種流體與流況之區別 : Netonian fli Non-Netonian fli Incompreible fli Compreible fli Stea flo 0 t Untea flo Irrotational flo 0 Rotational flo cont. Ieal fli Inici fli, Non-ico fli 0 Real fli ici fli, ico fli Laminar flo 層流 rblent flo 亂流

11 3. -D ler' qn. alon the treamline 3 因為是 Inici fli 0 No ico force 無需考慮黏滯剪應力所受到的力 :rere,grait rere force: A A A Grait force: W A Streamline ir.: W in A A 4

12 F F m a A A m A a Recall Chap.3 A A A 0 or 0 -D ler' eqn. alon the treamline For Incompreible fli: cont Bernolli' qn. alon the Streamline Interatin -D ler' eqn. alon the treamline contant H Bernolli' eqn. alon the treamline Amption 適用條件 : 0 Inici fli 理想流體 cont. Incompreible fli Alon the treamline -D tea flo 6

13 Bernolli eqn. i a efl relationhip beteen,,an here H otal lhea 總水頭 prere hea 壓力水頭 eleation hea 高度水頭 elocit hea 速度水頭 7 5. ner line L an Hralic Grae line HGL 8

14 ner line L otal hea line 可用 Stanation be 量測總和之連線 Hralic rae line HGL ieometric hea line 可用 ieometer 量測總和之連線稱為 pieometric hea or hralic hea 9 6. Work-ner qation 0

15 Mechanical ork-ener principle: Heat tranfer an internal ener are nelecte. W here W the ork one on a fli tem W t t the chane in.. an K.. of a fli tem For tea flo an incompreible fli: e A t c.. m m here e m m t c.. A A A W t :o part Srface force: <i> Normal: prere <ii> Shear: friction W t c.. pa A A oer F

16 Mechine ork: rbine t W mp t W here fli of eiht ener etracte b trbine per nit here fli ener etracte b trbine per nit eiht of fli ener ae b pmp per nit eiht of t t W 3 Work-ner qation oer: U.S. nit hp lb ft 550 or 4 kw J 000 or SI nit

17 D ler' qation D ler' qation Withot icoit No hear Onl rere normal tre an rait bo force F 5 F F We kno: Dt D t a Dt D t a Dt D t a a ma F 6 a ma F t a

18 a ma F t a a ma F t a 整理如下 : Dt D a 7 整理如下 : t D Dt D a Dt D a 如令則 k j i ˆ ˆ ˆ, 0 故 ler' qn. 通式 D 故 q 通式 Dt qn. of Motion or Momentm eqn. for ieal an incompreible fli can loe 4 nknon: p 8 b 3 eqn. of motion 方向 an continit eqn. 0

19 8. Bernolli' qn. in flofiel 8. Bernolli' qn. in flofiel Interatin ler' eqn. for incompreible fli an tea flo p p p 9 0

20 H Interation: Bernolli' eqn. an to point in flofiel ali for ler' eqn. 0 cont tea flo irrotational 0 If rotational,onl ali hen 0 treamline fnction Bernolli' eqn. onl ali alon treamline in rotational flo.

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