Table Of ContentSOLUTIONS TO THE
CLASS 1 AND CLASS 2
PROBLEMS IN
TRANSPORT PHENOMENA
Department of Chemical Engineering
University of Wisconsin
Madison, Wisconsin
New York ~Lendan, Jehn Wiley & Sons, inc.
CHaerer 1 — Checked by TJ. Sadowski
Tieo methods of solution art given in the fexts the tosetit theory merhad bavec nn
Eq. Lai, anct the cermspanding stnits meitod eaud on Ag. |.a-1, The kinetic ‘heary
method fs more ncarate, Calailahons by both methods aie summa
rp Nee
Resid vineriy fep t
ety
Consbeosts feats Tabla, Bs
[Sex Pea)! et CK:
1
pe 26692 aE
o.o2n23
wcol aay U8,
0. oLT4t
Hieotl Ban. 13
TCH, | G08} Saaz
the observed Yale are: (eounseps, Na (201iSip> , CH, Casing ep, ma gum
wh Take Cie,
LB Calewal
According ty Ey. 14-20
yy eae
ul* taal
0.4] oy Yep Loe Mae z
eB [t+ (Re) CEG) 4] © eope
1-1] then gives
(3) Fem Taole 8-1 we find that
IO g cent seul. Hence:
Pet pipe = (W000 + 14/17 (3.520197) = 1.40
(Pe VT = (460 ean 7 (2 6.2K1RD 232,
Hone, the predicnd viscosity 18 We pl Be = CLORYCERG WUE) = L154 107g cnet sect
(3 Fem Table LI-Z, 9c 20%. (AHF), pt nL Tewion tt g om 15
Tee IZG2 °K , pe= 38S atmjand Hes |6ox
Fen fig. 13-2,
for the fal iss op Pe GMa tp CUlabiaiedd cose, gS Lt, elemee dhe predicted veumily
He PRBS = Gays.) = 193 x4
gem tec!
fie
LD Eotimstnon of Lagu Wicasn
fay Bquanen
P EY 2132 BI3-2
1 p Gert oaaas | oarey |
: Y= ip Com? g-oai) ior | ese
| AEing CEng") at nownul bang pt) 499 | 484
BU ny = MBC y Coan geeneie | @982 | 9.98 |
exp 0408 AT yoy (RT S.¢on% | Léo eit
> zaro*| aia xne*
1 Peet
(b) Use 4 nSo2 taget: (Hee Tye ata)
At 2Teate aE Abn} exp OME Os ATR ae "
AL Seah! fm CURRIE) cap Coa =
Sumoniry of resus: tote
Cinsersed visiasicy Cap akat
Predins uy Eh, bE 237
Proeiclrel By Ey S18 ays
Bom eyachans give pane paditaas Task le net Saepriaelg inasemash as Ui, Copii
Frenne By Si
fae. aeinct held flor walle, nor fom mask asseutased jake
ji B34 WOT KETED) =
F (eZee
From FQ. bA-& tm mean frre path is
Op TP @rostX2is.2 .
VEwdipN ~ Jem (sR (i) (eonen OF
Hence the mean fice path is (4.3410 / C4x10F) = B10 molewular dram
under these aonditians. ba the fiquiol state, on He our hand, the tarrrspondyay
Talo umuld be of the ondir of mengninuae af or en kes than
anh
ALF Compartion of the UyeharaHlahon Chark with Kinetic Thay,
@) Combmedtion of Eqs. Ht and ef gwes
HO. aweqax ict YE
Vian Bp
in addition, fom Eq. LA cit we know that On aT fe
The calontutions. fr ite kiricks. thebey "plat aie sumnvnarsind below
Ors
nage a2IS
age 0.88:
2s 0.85
zee 2.4
B40 ! oO
5-08 133
by 8S
400 ele
Heer pict and the Uyehara —
Ay esuty er seen in the figure beth Ha kind
wlaisor plot predict essentially tie Sar kesparahue captncanceet vfiunity, O41 Seen
by He Strailer shapes of Hae hao cares:
1 Using on aretage alte far the vate of the ordhnaks of the he curves,
get
we ge: pe
pot hi
whet te] gq cet! ater A, and ID [1 %,
in raterapoies we get
Being for
by Ba Aer grt:
ano Te Loe: Yh | 2 594 MeL
2 gies a uneffrued of GLE bach is ofursarie Idantial
Estineeriin of 9 be
Bq. [4-18 gives:
pe 42 mt Te [ast teyp.7% 1%
Tham MMe pe To
Thi Shewls be compara GUA Ey. bod in alain Ba samentad eoivenk is 270. 19
Witte of Ho opp ainialt cwhkmaf Egy 64 tye is
ar fe be pislermeds
» Uyehare, apd Waiter, reathon:
4..G — Compamon ofthe Sinpe Kinetic Theory with the Exact hon fr Rigttipnercr
When Eq. 14-4 15 written in terms of the uniFs used in Eq. £418,
and dis assured 4o be the same as ot we get
= 2 Sf
we gy, oe
2 (Be xioct
“Sr (6.023 «10
aT
30s ) Ue ay
= als xior® NED:
Eq. (4-18 reduus fo the same form os that above (by setting O.p equal fe unity)
but the mumerical comiant is 2.4673 # 1075, Hence the sinmpie lunelre Heong
law by souk 32% for rigid qhers.
CuapreR 2 — Checked by V.D Shah
Z.A Determination of Capillary Radius by Flow Measurements
Sale the Hagen-Poiseatile formula for R to get
ev afin of sue
“dp % Ap
in which Y= p/p and ur = pG@. Using mks units we subshhae info this
Forrnula, te get
a (21416 (4.329 x 104)
- “3.185 aioe) = ett mor OLFST tam,
The Reynolds number fior the sysfern ts2 frais anita une here)
Re. Pe. 2 ( ) 2 aatew) _
i z Ydog nd Kasse:
pron
Hence Re = 66,0, and the flow (S iammar (this fustiBes use of te Hager.
Poiseuille Ine. inamuthas Le = 0-035 DRa - 6.35 on. , allowane for the
end effec would net change R by more Phan a factor of
= 0.938
Je of Flow threugh an Annus
We ux Eq. 24-86 ta which
SARS. OAs
(136.8
~ B80x10* Ib, £07! sect
(5.2 ley a AAI pometn I6et AE ae OD aaa x iat
CLL mC it) = O.0407 Fe
Thensubsithaton inko ER 2aielb gues
Qe Est 210% Ibe A
y Car fe)
Te verify thot it wes proper fe ust the Jammnar flow formula of 64.2416
we compule the Reynolds number:
Rex ZR Code
BF
= 2 (0-108)¢ 80-3)
® (6.0317 (3.3 x10 9
ZC Lass of Catalyst Particks ma Stack Gas
@) Renrrangement of Ep. 26-16 gives
My Dae) g / 18 p
in urnch Dis the sphere diameter
When vy, ts argo than 4.0 fb sec”
loamward, then the partick will not “Go up the sinde, rere we
sian to ind that vaheof D for which vp LO fr seen! This will be the
neucieare diamcer of parbiees Hhut can be lest
Using cgs umils we gt
, CL ft seco C42 me fA 84 em in) BOS cre seat
P= (0.045 ib, ROWAN g tbs! 2 «2849 [fee cme)
2 «10+ g cm?
Dan. = [ees - | Peeeiee
&-9)9
(1.2 - 72x10") (981)
= fraract
Lie iot em = tO
microns
BD) Eq. 2b-Me ts of came valid only for Ret Oud
() Eq. of Ny
appited opproumately Ups aboul Revd.
Re
alirough it moss be
For the syppien at hand.
Dyp Liebe H
: al
25 (0.2 #1079)
S = O43
(©. d0028) y
In Ghoplor & , methorls are giver for handliy flow armed spaues fro Rea 7b
equation:
= pg co B
dz Fg oer
which may be infegaled to ghe:
Vy, = pgh op + C
Inatmain as Na mometuin is transfowd ot Zed, thon
we have Tp, = 2
ip be:
ok that pian
This boundary condition enables us to cleteremine Cy
=~ 9 gh coe
ana hence the momeniven fine drsheburion ist
Ta, = -9gS esp Tt - (28
Note Hat [he momeniuen fiux is mv the neyative X-airechen.
Incerfion of Newton's lav of viseosthy Tz, fk Ge dR) ania the
above expression then gitts the dlfferentialeguanan fer thie Velocity slsnibubon
This forst-ordae differential equashiors fs easily integrate $n give
ve = (238): coo G _ 4)
the constant of intepation, Ca, being ze becaux Vero at ©
Now we mole that Z and x are Fetal thas
= 1-0)
ie)
where XG fhe Goorthaale used 1 $2.2. If Ha above relation is subsitheed int
the velocily distbubon we get +
= (9h8¥, x : f fN*]
vo (eae Lage ofa-28+ (HT
twhich, upsn simplification, beromes?
ve = (Sine Lt -GY)
which is Vre same as FQ 29-6, This just Wlushaks that du choice of condsnake
Sysiern mates ne differen we the final arsevers
(8) Substihakon of Eg 22-12 ins Ey 22 geen
Bye PD cos
pew Gpjee
|miegration twice gives
P2) cos
v= ER )eoss
Application of the botndwy conditions
Bo 4 Ak x0, We/dazo
BC 2 Al eR ye
ites Hw Simullanous equations fir the integration @rehants Ce and Cat
