Unit 1-Fluid Mechanics

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

G5>>2)1)1

V@HT 1 ^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

IJGFETH\FU

Of`fzak Ijgfeth|f

7 Ti c`iw+ v`dfzuta`d a`d a~~kx tbf mfauvzfmf`t mfauvzfmf`t il tfm~fzatvzf+ ~zfuuvzf a`d ~bxuheak ~zi~fzthfu il lkvhd.

U~fehlhe Ijgfeth|fu

7 At tbf f`d il tbf v`ht xiv ubivkd jf ajkf ti 7



khut tbf tfm~fzatvzf ueakfu.



ei`|fzt tbf tfm~fzatvzf ti Efkuhvu "· E (+ (+ Labzf`bfht "· L (+ (+  Z(+ Cfk|h` " C ( ueakfu. Za`ch`f " Z(+



^ ( + Atmiu~bfzhe ^zfuuvzf " ^ atm dflh`f ^zfuuvzf " ^ ( atm( + Oavof ^zfuuvzf " ^  " ^ O ( + Ajuikvtf ^zfuuvzf " ^  "  ^ A ( a`d \aevvm \ aevvm " ^ | (



eakevkatf ~zfuuvzf oavof vuh`o tbf lizmvka oh|f`.



dhllfzf`thatf mauu df`uhtx "  ρ (+ u~fehlhe wfhobt "

ψ  (+

oza|htx " u " u ( + u~fehlhe |ikvmf " | ( a`d |hueiuhtx. 

eakevkatf lkvhd ~zi~fzthfu vuh`o tbf lizmvka oh|f`.

u~fehlhe

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

G5>>2)1):

H@TZIDVETHI@ H@TZIDVETHI@ TI LKVHD MFEBA@HEU Lkvhd Mfeba`heu - H`tzidvethi`   Lkvhd Mfeba`heu hu a ufethi` il a~~khfd mfeba`heu+ ei`efz`fd whtb tbf utathe a`d dx`amheu il khqvhdu a`d oaufu. C`iwkfdof il lkvhd mfeba`heu hu fuuf`thak liz tbf ebfmheak f`oh`ffz+ jfeavuf tbf magizhtx il ebfmheak ~ziefuuh`o i~fzathi`u azf ei`dvetfd fhtbfz ~azthakkx iz titakkx h` tbf lkvhd ~bauf. Tbf ba`dkh`o il khqvhdu hu mveb uhm~kfz+ ebfa~fz+ a`d kfuu tzivjkfuimf tba` ba`dkh`o uikhdu. F|f` h` ma`x i~fzathi`u a uikhd hu ba`dkfd h` a lh`fkx dh|hdfd utatf ui tbat ht utaxu h` uvu~f`uhi` h` a lkvhd.

Lkvhdu a`d tbfhz ^zi~fzthfu

Lkvhdu

H` f|fzxdax khlf+ wf zfeio`hf tbzff utatfu il mattfz7 uikhd+ khqvhd a`d oau. Aktbivob dhllfzf`t h` ma`x zfu~fetu+ khqvhdu a`d oaufu ba|f a eimmi` ebazaetfzhuthe h` wbheb tbfx dhllfz lzim uikhdu. Jitb azf lkvhdu+ jvt kaecu tbf ajhkhtx il uikhdu ti illfz a ~fzma`f`t zfuhuta`ef ti a dflizmh`o lizef.  lkvhd hu a uvjuta`ef wbheb dflizmu ei`th`vivukx v`dfz tbf aethi` il ubfazh`o lizefu+ A  lkvhd hu biwf|fz umakk tbfx max jf. Ei`|fzufkx+ hl a lkvhd hu at zfut+ tbfzf ea` jf `i ubfazh`o lizefu aeth`o a`d+ tbfzflizf+ akk lizefu h` tbf lkvhd mvut jf ~fz~f`dhevkaz ti tbf ~ka`fu v~i` wbheb tbfx aet.

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

G5>>2)1)5

 H@^VT 

1.1

TFM^FZATVZF V@HTU

Tfm~fzatvzf ueakfu azf dflh`fd jx tbf `vmfzheak |akvf auuho`fd ti a uta`dazd lhrfd ~ih`t. Jx h`tfz`athi`ak aozffmf`t tbf uta`dazd lhrfd ~ih`t hu tbf fauhkx zf~zidvehjkf tzh~kf ~ih`t il watfz. Tbfuf azf zf~zfuf`tfd jx tbf utatf il fqvhkhjzhvm jftwff` utfam+ hef a`d khqvhd watfz. H` tbhu v`ht wf kfaz` biw ti ei`|fzt tfm~fzatvzfu h`ti Efkuhvu+ Labzf`bfht Cfk|h` a`d Za`ch`f ueakfu. Tbf Efkuhvu tfm~fzatvzf ueakf vufu tbf v`ht dfozff Efkuhvu "· E (+ (+ wbheb bau tbf uamf mao`htvdf au tbf Cfk|h`. Tbvu tbf tfm~fzatvzf dhllfzf`efu azf hdf`theak i` jitb ueakfu. Biwf|fz+ tbf fzi ~ih`t i` tbf Efkuhvu ueakf hu ubhltfd ti :?5 C  :?5 C + au ubiw` jx tbf likkiwh`o zfkathi`ubh~ jftwff` tbf Efkuhvu tfm~fzatvzf a`d tbf Cfk|h` tfm~fzatvzf7

T "¾E ( = T " C ( √ :?5

…"1(

 Z(( hu Jx dflh`hthi`+ tbf Za`ch`f ueakf+ tbf v`ht il wbheb hu tbf dfozff Za`ch`f "" Z ~zi~izthi`ak ti tbf Cfk|h` tfm~fzatvzf aeeizdh`o ti

T  " Z ( = 1 . 2 T  " C  (

…":(

A dfozff il tbf uamf uhf au tbat i` tbf Za`ch`f ueakf hu vufd h` tbf Labzf`bfht ueakf+ jvt tbf fzi ~ih`t hu ubhltfd aeeizdh`o ti tbf zfkathi`

T "¾ L ( = T " Z ( √ 4

…"5(

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

uvjuthtvth`o Fqu. "1( a`d ":( h`ti Fq. "5(+ ht likkiwu tbat

T "¾ L ( = 1.2T "¾E ( # 5: Fram~kf 1.1

 C . Ei`|fzt :>>·E  :>>·E ti ti C  Uikvthi` ti Fram~kf 1.1

 C 

= ¾ E  #

:?5 = :>> # :?5 =

4?5  C 

Fram~kf 1.:

 L  Ei`|fzt :6> ·E  · E ti ti · L  Uikvthi` ti Fram~kf 1.: ¾ L  =

5: # 1.2¾E 

=

5: # 1.2":6>(

=

42: ¾ L 

Fram~kf 1.5

 L ti Z  Z Ei`|fzt 52)1)4

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

Fram~kf 1.4

 L ti Z  Z Ei`|fzt :>> · L ti Uikvthi` ti Fram~kf 1.4

 Z

4 # ¾ L  = 4 # :>> =  Z 46> Z ti C  ti C  Uikvthi` ti Fram~kf 1.6

 C =

 Z

1.2 46> = 1 .2 = :6>  C 

Fram~kf 1.<

 L  Ei`|fzt 41> C  41> C ti ti · L  Uikvthi` ti Fram~kf 1.<

" C  √ :?5( # 5: = 1.2 "41> √ :?5( # 5:

¾ L  = 1.2

=

:?2.>2)1)6

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

G5>>2)1)<

AETH\HTX 1A

TFUT XIVZ V@DFZUTA@DH@O JFLIZF XIV EI@TH@VF _HTB TBF @FRT

H@^VT…! 1.1

_zhtf tbf lizmvka ti ei`|fzt tbf likkiwh`o tfm~fzatvzf ueakfu.

·E ti C 

 L ti Z · L   Z ti C 

1.:

Uik|f tbf ~zijkfmu jfkiw7

h(

Ahz f`tfzh`o a wft uezvjjfz hu at 165 · E . _bat hu tbf tfm~fzatvzf fr~zfuufd h` dfozff Za`ch`f9

hh(

Tbf oau utzfam tfm~fzatvzf f`tfzh`o a lajzhe lhktfz hu 41> · L  · L . _bat hu tbf tfm~fzatvzf fr~zfuufd h` dfozff Cfk|h`9

^ZH@EH^KF EI@EF^TU IL LKVHD MFEBA@HEU

LFFDJAEC I@ AETH\HTX 1A

1.1

·E ti C 

 C = ·E # :?5

· L   L ti Z

 Z = 4 # · L   L 

 Z ti C 

 C  =

 Z 1 .2

1.:

h(

Ei`|fzt tfm~fzatvzf lzim Efkuhvu ti Labzf`bfht.  L = 5: # 1.2·E  · L = 1.2·E   L = 5: # 1.2"165( · L =  L  = 5>? · L  Ei`|fzt tfm~fzatvzf lzim Labzf`bfht ti Za`ch`f.  Z = · L #  L # 4  Z = 5>? # 4 = ?