Lecture_16_notes

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

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 03/11/2012 for the course CHE 374 taught by Professor Davidlignell during the Fall '12 term at Brigham Young University, Hawaii.

Page1 / 5

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online