SOLUTIONS 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