1) The document provides equations for incompressible flow between parallel plates using the no-slip boundary condition and cylindrical polar coordinates. 2) It solves the equations to find a valid solution for the Navier-Stokes equations, obtaining an expression for pressure and velocity. 3) It discusses that the solution is not always valid for potential flow cases where the body is an irrotational solid.

1. O
O

2. Assigamet 2
AE21 Foo8
Ameeah Kuma
Guesi
V, Snmls d= 4Cm ch = 5 cm
d 6cm dg=9m
a = 12om/%
on he ConsAvatton ef ma
ALVt AV, +A; V; A4 -C
Cons1ta2tn Inchease y 207. incHeases Ga by lo
ee
23G4 -
Ca =
aom/h = A4V¢ Va = 20 niy
(O-03) 2 36o
Vaa S. 24mls
2x Az Vg S.24 xA = Q4.
V3 12 36o
2 Az
2x(Ovo6)
N35.9m/s
om eD
2
(o.04V (005)x5 +6o
36o0 36oo
(O-o5)>5
36o0
Va-S.45
m

3. Sues
u- Umur -
R
in = O.
um the onsenvato massin in &tta d
in pdA=out
o
2
8in U. xA out CAmax
= U. TR
8out Umax
/ do d6
de
O
nar -den)
et 1- = -d=d
ot 2nUma/-) 2'e |tR+R)da
27 maa R 1 - d
F TOmaa
8
= 27 Umax P (
49UmanR
60 42 mas
6o
in out Uo
Cmax 60

4. Ques3 U= U. 3n- n
y Conseruvatom may
+ Sout
1 UodA = U. s)
SSu da
s
2
S S
-
=
SU.S
U.bs S 0,S +
8
h 0 , 6 S

5. Ques U= V= y-2 = O
ConsCvatom o ma
v.V=0
Sata t o =O
iven o dy ace Ochedo
to incompkessible monentum euaton -
at nj
F - Com pment
3+udu avdu = k - P y
d
du 2
dy
n 2
= 2p(ay+
P =
2 p(1y2)dt
P- 2p ( D)-
P
Compenent P +
- ud+v
dv=-2n P-4y2-2g)--3+a (a+)
dy
d 2
dy
d - 2
OP -anyt2y3)-

6. m eq P - - 2puaby) g)=-2pry+d)
2
2
eg trg eq) -2
-2pny + dIG) =- 2p(n'y +y')
y=-2y 3
9)=-P4tC-
2
Put e ineg
Glven Tha at (o, o) ptesue = fa
P=
C a
P-
R-2(r)*
uesS UOu V=lo , =o,G=O
Continuity euato in CompHessile o
V.=
O + O +o= O
Contrauhy eguatom atlies 1 any O 6.
Momen him eg UattOn
Pdudu + Vdu=-2P + T
d
0 Component-
y
u O du
Chn
Plabm)
P (ab)dn
d
2

7. mb ent o l o
uU +Vdy
(oby)---
e O
3P =
d'()-
e (7y) -paby
/9) =pabyc -
P = - P a l a +
Paby+ c
2
P-Pal/y +c
2
Thslouo On exac sotono Nouie-stpkes
Canttauty tguations o ony bie. a l s ate
donoeeamine exact Soutton.it Car hold any Value.
dues6 V-k - Kzk
Conttnuily euat
K+K - 2K
T Satts'u Contnuly eguaHa

8. mmentumm to uations
Jot n Com ponent olow
u TVuou P ph+
u-k -u = o
P-3
F
jP=-perdh
P- e ,2)-6
o y m panment lo
+ u V v
d
wdv)--3P- T,+
aVo t
-
aly. z
P * s ) - O P - P k y d y
+9(2)-
P 2
Z- Combonent ouo -
du-
2 0 = -2k
-Pg-4pkz
Pt4-z) =
- Pg- -

9. om eg
- =
-
g')-6
euattn e
) = -
Pa
g()=Paz
- 2 pke+C -S
inset value o ga) in eg
Pa -
Ph +J(2)
2
--yk+Py+9(
2 2
-
-29 Kz+C
-2E(-yr 42)-Paz*c -6
This ield sa valid &dutn to Nauien&ttoke 's epuato
Ond euahan i e 6)
T VXV=O it i ino tatlnal oteauise rala
Cn -2fz
=1(0)-jlo) + lo)
O
x u o o4atonal

10. Sues
+2
Suest2 *y* KY 2D
intnbrcesible velo city
RtenHal.
n
+2m 2
-+2x
n
22
= 2 2
2
n
2 (
v =o s net alooys thue it body tue enlg hoty
The i 9hetatonal excebtlo,o) and =(o, 0
low is net valid oluton CanseUator ofmas.

11. Ques8 n Compesibte lo in Pola oerdihake
Vs = k tos91- Ve-ksne+
Cinuity tquatan n Poah oshclina te
) ) + lu) - o
z
so (
260)=2h csel
U - gin0/1+
uo) -K e
aakoso
LU) + (4e) +2)= 0
+O
SaHaDes conttnuiy eguatton
VH= kcoe
Dimenon o mst e Some as Va Gnd has dimesle
ame as
-1 -V.-LT-
e6 coso- = o
= n2
2n-)
Cs(-%,

12. ebxesent. a Cy lindles a d h
ues 7 U =
4Umax h-8 V =o
h
Woll emboature =To at both walk
-h to)wall
Using ncm biessible louw eguat
pDhi
Dt
Ti
DP
Fon Btcady low hi o T- T)
t
Z
Dh
u v
DA
- )
VE=o
otken Cmnent uill
T
dy 2
4 mh2y)
h
oy
d2T-16
24Un (h,4hy +
4y
dy
dT -6LeUau ( h-2hy+4y3)
+¬,
dy
kht

13. T -l6 u
( y)+0g*%
kh
Doirg 3 CamdtoT(y-o) =To,T/y-) = Ts
Iven
Tuo = C2
Ch =-16uOnar
( )
- - B
k 2
Omax
Ty)-To - 8 0na
- 2 4
344+
2
hues1o hest Txonger cogllicien = g =hASTT
hco ousale(374)
A- ace AMea m)
ST- Tempeatuwe dileemce k)
h P,Cp,V)
has dimensim M°L°T°E°
3lhP,Cosv)=f
h= MT-36 [p] -ML? [c]=L
v =LT
M'LT- Mro- [ME3]"[E]
MLOT G M +
-3 -2y-z -3+2yrz
C pooning otk LHS PHS
3h+2ytz

14. O-1
3 C=o 2+C =3
+a-o
-1 -&= o
- h p "C v
3a +2 +c = o
3+2+ c =o
2 + = -
3 PCpV
-2+C =
-3
C=-1