Lecture_16_notes - ChE 37 4—Lecture 16—Laminar Flow 0...

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Unformatted text preview: ChE 37 4—Lecture 16—Laminar Flow 0 Outline — Chapter 8 takes us through the next exam — Laminar Pipe Flows (today) — Turbulent Pipe Flows A Minor Losses (valves, fittings, etc.) — Pipe Networks — Flow Meters. o Reynolds Number (Re 2 pDv/n, or Re 2 Dv/V). YOU MUST KNOW THIS. — Characterizes pipe flow >k Turbulence transition at Re=2300 in pipe flows. * Ratio of inertia t0 viscous forces, or ratio of diffusive to convective timescales. l o Entrance Region . — Flows must develop: Steady, but changing downstream until fully developed. — An initally uniform flow hits a no-slip condition at the wall. To preserve mass, the interior region speeds up. — A boundary layer develops (BL. separates region where viscous effects have been communicated, or felt). — Entry Length: Lh/D : 0.05Re for laminar, and Lh/D % 10 for turbulent. >i< Must correct for laminar, but ignore for long pipes when turbulent. — Pressure drop greatest in the entry region. 0 Velocity Profile 7 u : u(7‘): 1-D problem. 7 Do a force balance on a cylindrical shell: Pressure and viscous forces. — Take limit as A3: and Ar —> U ~> a PDE. *_3_P_i3£ 8x7r8r‘ — Left side is f(x) and right side is f(r) so each side equals a constant. * That is, dP/dx is constant. * Solve for 7' with BC. 7' = 0 at 7“ = 0. _id_P£ *T_ d$2 — Now use T : —a% (note the sign: 7' is + to right, but du/d'r is negative. — Insert and solve for u with BC. u : 0 at r = R. * W) = As: (a) (1 ~ O Parabolic, u(R) : 0, u(0) : am”. a 1 - _ RZdP_ ‘ Uavg # —— aumam/Z — Note: navy is constant over length, so integrate over length: (**) P1— P2 : AP : (Note sign). -Recallr= (325% >Tw= (Zifi: (:35)?- * Integrate over the length —> 4710 : A—fD. - TRADEOFF BETWEEN PRESSURE AND FRICTION. —— Ratio of friction to inertia: 471—8T1_M_ _ -. 4: m i m _ [43qu i f _ the Darcy Frrction factor. - Works for laminar or turbulent. — For laminar, insert for APD/L —> f = 64/Re. class l‘=— Law-w; PM» FIN .W cw- ? 124%» M {mek may.“ exam ( ’Léx‘bflq" (ToJa-/‘) —Im4ow~l may); ‘ Fr'Pr Hon 4J1! 0“ le’f‘l +wt4’ “' Tia/7144A 'Piyr FUN " Min 1055:”) -* Valdzgf N Pi 7( Met-AMPS "’ I: [Du-6 M¢+mj '~ 4.2.6. inwmfigeemlz, I )F Canter} C Frceéw Wrap Bald—\rfiwg) {\(IZPM ’ZC\[VWD’¢’5 '5”: V94 Cla$9 $5“) '2 éfau’); : Q, ., FDV A? D 9 H00 Ctaepgi‘a‘ee' «A L&M;“M a? ’I'ML-Jwr‘. I UM'IAM " g+(“"‘l;w) MD+IIOW f CA,‘\0+I‘C/ Qandom) a [MDO’C \ v peYnDH a 5.6 I “fic{(m-t ’2‘, . f2; ékMAc—fmi'zco Pith) w, , _ I ~ _ - ‘. ' I26 ’ IDDV 'DV . 7 a? .- 677 P‘P’Mt’ ’5 “>171— CLmAcvlwéHC '9 [15"an (Jen/L L . N04¢{(éu1M\Du¢,.-I's “A? bk : ulAé /7>\J l ‘ ‘ \ :E‘ :5 a fleet ~27 (24 3g 144.4 224+: 0" Conwdvdfi/ (7‘1. ac DH: Ma. - €01 Rt 3 (“D -——"7' 9", [ODD {I‘mtfi 1537;“ {o DLFcW t:L‘¢’~ fie Canatc", 01)”? L (an aka .204: M Lt“sz 904,4 [Ye—«H0 - IZ{ -'"‘"” {wade /\ Q¢ (y. Vé‘ EM~H¢ 7 Cm 6’ “SHPRI )0 4‘1: I»; w 270/ 000 Hedi”: [OMPA ) é H ,j ({g’ 000 um ¥au£¢4 Q l ’ [/1 ” fl“? I Lamina», ;5 [ix-41¢ Fairy“, 7549* 7L5 E n-h‘adéf. iom ' - Fl,” M M + Doug I07 ' pttzw {fin—1 Cepétt) “ Unf‘Pmr-x Flo“) -—-'r “‘9 9W7 ‘71 ‘0‘”! -w~LLa-"0 , 6t¢+m ivxéltésg/J ’ 30““‘3‘47 hymbwehr mtg-L in yaw, .- L'H 5 L—H ...
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Lecture_16_notes - ChE 37 4—Lecture 16—Laminar Flow 0...

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