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Na
Konnas nday lage Oe a at plate
eahall deaie a te elakimu t he elocih-D
dlnhuim_eithin the beundaylayes and the
Haicknes Df-Hae veloity bounday aye 4
Lanainasler e a hkt SwpaLe /plak
Na
Lonaides hak a tid ef-deeitPand Vistosity C
veleity Hae lonin uid eutsiele ha lelaiy-De
Les nres lat plale a pPane Supare ha
bundany aye is Uao e Shream velaaty) The
U
heeunda ez 4 thickness Soma neas hi SupaLe
the plotë and a heiqht y_dhue Hho SweuLe
elocih 4 uidis Ux_Assumethat Hhe
J
uid is inlam rea hle andHo is Steady
nsides a Conm wlunae H the Hudbundeo
Plane 2and 3-4_at_disteote x and x+ dx
4h Leading e de G He plae, tho sulleue
and aplane 2-u panallel h SuLae cCund at
a_distanLe Dit ond to planeA panaLLel w
hplan papes and tunit dirtenLe apant_
and
he elouty Lampunets_Alyin Hh X ineuhim_
aue Aoideid ancl n Mal 0 hotsaU aue
hegle cked
T s osumed Hact _Jz 8:e he umhololunme
isSuPiientyhighSoitalay2 nclse abeundasy
Jayes
Date
Page 4
dx
2
Ux
3
Ne Ahaall Conaides x- dinethm mDmentum and he
X-
clinethm rt e
At_PJane 1-2, h max Ho tk thmng altmbp
thickness o at aictante de HhaSutaue
A7sauea fr
m:S u
A 1)
Tot Amás tloo thrgh plane -2 into nh
olunaghrtng planeid is
ud
The rtte ef
elementM Sm S
mom enum o n hmug 4
SChdy).4 f4 dy
h e 8f_Mtmentum o into 4h0 wn
P- mux
olume tng lane 1-2 1s
/IYE
h eue mas Hos out ie ho rateat WhicEu
maM eut tho nbo1 wlume hwng plen 3-1 b
gve d
Chany ra E
fu d + d y x
ut TOtehageove
a eemet
enh
ud t+A
The Yale momentum e ut theuge pa
3-41S
Pudy4x
dx
la Linq into CLLCDunt the fect hat no _mas lan eukes
he enb nlume thml a colid ell Hheeddihnel
mam{leud 1n ereMim V 3 oves that in H
Conueein mek
reuim AA pe heaw
mat eake hnag Plana2-u
The Heo in thwat pJand 2- is
A pla eutsideHh boundabuLaye
hi enkeinq uelmuat hare a elsdhLa (m
Stream vei in te_X=dieshm
Iheee_He ae e wamentumL utO
umbo lum p Lenl 2-4
i
Pu y dx
Theotes etin4 n x-diaetim ca the
wlume a
Sheas fuce
Cwatinqou ha utade thePlakeTh
S fausling foce Cnd heepre negahe
CUnb
A Yeouhna Sheo
shean rey
(As e velecity qrealient is zeo tutside tha
ane zed
Thafare Preeued0 a renilt 4 a
diteace in pesune dp beheenplanla 3-y
nd 2 2 Ho eu 1 Hhe Velout uside he
beuundaylayes rtmais lonattnt Lene is w
Me graelicat in HoX-_dueLtin E0
And hehehore be zeso
ThAeorethe Ons Susfewe krte_Cuhnqio
wwundm s Hhe Khea foce/nste
Swyare o p.lnke qnedis
frrt
b
Tw (Idx ) dx
Abplyn_neotunS_Setaned a nmato
A &kad HeLo4hotnng a hol yolu
We hatJe
Page
m o m emtum. looput ef Lonko E
o lume
hetbrte eatea eneked on tha Cntol inlum-
nto_he olMolueisequal fo_fh
O 4 mo meintum ro
he Swmouncinge
o d X
Pudyoa-tsd
dx
d
dx
fud dx
Lince d lo
Puudy dx: Py,dy
Uo0
dx
o
udy -wd
Jividy dx
u-U dy
Pd
odx
Abtc ea he inleq2al mamluctum
he blunday aye umatn eunle
Condutiom
TheieLtim bet ond y_1lnao e
desie Xamna /Shcamneloo
lat plak
ASsume thatthe veleity le 1- eletion
eticen Ux and be Ha mm en helera
ASSumd
Uy o + + +s
hese Qo a, a Cndaz aue Cowotsnt_Hhat
Gn e eraluated pam ho aeundany Lnditiomk
h hncdany mdiims ae_
S UxeUao
S 0
As have
u tz
JZ
ul u
elassMAte
Date
Page 9A
Since at SS
Also Ne hare
Un U +
UxE O and UE O
at JE0 Ux:0 CLo O
Un ay+ + 9
at24Y+39ay
20t63
at 0, ux
2a2 09 Q0
U
at30sY
OD
at S
30,SS S
SCr(13
.Q 3gS
E
Uos
he latim 1S_abhiable bvesa Ange
KYk&
hen
Subshntn ahue Veleih motile io Intera!
mAmeutu eg he in Karal ine4 lan be
aluakel poalaminas nundasy loyes h
Lnoidesung he nge y <£ ane S<yA
Sepaaatel
fts-Uxdy-
oTeu)
- U
S
-1 Y*+2,1,
ASSMAT
Date
Page
ion
S 23
3qaa SS
280
On
3 U
2
2-S
o
2
DHpal mamentym eg)_belemeA
3 Us S T.3U
34 yo 48=3U/
280 h0
3Pu M_
X +
40
3
1 3 e dS dx
Dhle ceting abvve eg)
1o d
73 SUoo
C -
at X=0, S-o
4Oe-+
3
140 X
3
S 80UX
I3
SH64
Inudbplpry bot Side by weweet
Nex
Nex PUoX
hiction sefficient fis defmed n Hhavati
LJalL Shear Shress ho the_podutt of eeih.
head Gne denoi
Sint Cwrttu
and
TuoS ven Cw: 2
qnd S 464
= 0 323uUan a0P
O323uho Uaos2x
P L
0-323/ PHae l -
fUoX
0-323
0 646S
kex)
s oJotal Value e e chon Lcelhuen
Ot_a distante X m e_XeeÄng edge
3 2
8Nke
uhn otpusd

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MATERIAL 7.pdf

  • 1. Na Konnas nday lage Oe a at plate eahall deaie a te elakimu t he elocih-D dlnhuim_eithin the beundaylayes and the Haicknes Df-Hae veloity bounday aye 4 Lanainasler e a hkt SwpaLe /plak Na Lonaides hak a tid ef-deeitPand Vistosity C veleity Hae lonin uid eutsiele ha lelaiy-De Les nres lat plale a pPane Supare ha bundany aye is Uao e Shream velaaty) The U heeunda ez 4 thickness Soma neas hi SupaLe the plotë and a heiqht y_dhue Hho SweuLe elocih 4 uidis Ux_Assumethat Hhe J uid is inlam rea hle andHo is Steady nsides a Conm wlunae H the Hudbundeo Plane 2and 3-4_at_disteote x and x+ dx 4h Leading e de G He plae, tho sulleue and aplane 2-u panallel h SuLae cCund at a_distanLe Dit ond to planeA panaLLel w hplan papes and tunit dirtenLe apant_ and he elouty Lampunets_Alyin Hh X ineuhim_ aue Aoideid ancl n Mal 0 hotsaU aue hegle cked T s osumed Hact _Jz 8:e he umhololunme isSuPiientyhighSoitalay2 nclse abeundasy Jayes
  • 2. Date Page 4 dx 2 Ux 3 Ne Ahaall Conaides x- dinethm mDmentum and he X- clinethm rt e At_PJane 1-2, h max Ho tk thmng altmbp thickness o at aictante de HhaSutaue A7sauea fr m:S u A 1) Tot Amás tloo thrgh plane -2 into nh olunaghrtng planeid is ud The rtte ef elementM Sm S mom enum o n hmug 4 SChdy).4 f4 dy h e 8f_Mtmentum o into 4h0 wn P- mux olume tng lane 1-2 1s
  • 3. /IYE h eue mas Hos out ie ho rateat WhicEu maM eut tho nbo1 wlume hwng plen 3-1 b gve d Chany ra E fu d + d y x ut TOtehageove a eemet enh ud t+A The Yale momentum e ut theuge pa 3-41S Pudy4x dx la Linq into CLLCDunt the fect hat no _mas lan eukes he enb nlume thml a colid ell Hheeddihnel mam{leud 1n ereMim V 3 oves that in H Conueein mek reuim AA pe heaw mat eake hnag Plana2-u The Heo in thwat pJand 2- is A pla eutsideHh boundabuLaye hi enkeinq uelmuat hare a elsdhLa (m Stream vei in te_X=dieshm Iheee_He ae e wamentumL utO umbo lum p Lenl 2-4 i
  • 4. Pu y dx Theotes etin4 n x-diaetim ca the wlume a Sheas fuce Cwatinqou ha utade thePlakeTh S fausling foce Cnd heepre negahe CUnb A Yeouhna Sheo shean rey (As e velecity qrealient is zeo tutside tha ane zed Thafare Preeued0 a renilt 4 a diteace in pesune dp beheenplanla 3-y nd 2 2 Ho eu 1 Hhe Velout uside he beuundaylayes rtmais lonattnt Lene is w Me graelicat in HoX-_dueLtin E0 And hehehore be zeso ThAeorethe Ons Susfewe krte_Cuhnqio wwundm s Hhe Khea foce/nste Swyare o p.lnke qnedis frrt b Tw (Idx ) dx Abplyn_neotunS_Setaned a nmato A &kad HeLo4hotnng a hol yolu We hatJe
  • 5. Page m o m emtum. looput ef Lonko E o lume hetbrte eatea eneked on tha Cntol inlum- nto_he olMolueisequal fo_fh O 4 mo meintum ro he Swmouncinge o d X Pudyoa-tsd dx d dx fud dx Lince d lo Puudy dx: Py,dy Uo0 dx o udy -wd Jividy dx u-U dy
  • 6. Pd odx Abtc ea he inleq2al mamluctum he blunday aye umatn eunle Condutiom TheieLtim bet ond y_1lnao e desie Xamna /Shcamneloo lat plak ASsume thatthe veleity le 1- eletion eticen Ux and be Ha mm en helera ASSumd Uy o + + +s hese Qo a, a Cndaz aue Cowotsnt_Hhat Gn e eraluated pam ho aeundany Lnditiomk h hncdany mdiims ae_ S UxeUao S 0 As have u tz JZ ul u
  • 7. elassMAte Date Page 9A Since at SS Also Ne hare Un U + UxE O and UE O at JE0 Ux:0 CLo O Un ay+ + 9 at24Y+39ay 20t63 at 0, ux 2a2 09 Q0 U at30sY OD at S 30,SS S SCr(13
  • 8. .Q 3gS E Uos he latim 1S_abhiable bvesa Ange KYk& hen Subshntn ahue Veleih motile io Intera! mAmeutu eg he in Karal ine4 lan be aluakel poalaminas nundasy loyes h Lnoidesung he nge y <£ ane S<yA Sepaaatel fts-Uxdy- oTeu) - U S -1 Y*+2,1,
  • 9. ASSMAT Date Page ion S 23 3qaa SS 280 On 3 U 2 2-S o 2 DHpal mamentym eg)_belemeA 3 Us S T.3U 34 yo 48=3U/ 280 h0 3Pu M_ X + 40 3
  • 10. 1 3 e dS dx Dhle ceting abvve eg) 1o d 73 SUoo C - at X=0, S-o 4Oe-+ 3 140 X 3 S 80UX I3 SH64 Inudbplpry bot Side by weweet Nex Nex PUoX
  • 11. hiction sefficient fis defmed n Hhavati LJalL Shear Shress ho the_podutt of eeih. head Gne denoi Sint Cwrttu and TuoS ven Cw: 2 qnd S 464 = 0 323uUan a0P O323uho Uaos2x P L 0-323/ PHae l - fUoX 0-323 0 646S kex) s oJotal Value e e chon Lcelhuen Ot_a distante X m e_XeeÄng edge 3 2 8Nke uhn otpusd