Lecture_29_notes

# Lecture_29_notes - ChE 374~Lecture 29—External...

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Unformatted text preview: ChE 374~Lecture 29—External Flows—Drag External ﬂows are flows over objects: cars, wings, buildings, etc. Objective: Understand and compute drag forces on objects. — Concepts: Flow separation, Lift, Drag, Drag Coefﬁcient, Laminar/ Turbulent. Drag is the force a ﬂuid exerts on an object IN THE FLOW DIRECTION. — Lift is the ﬁerce a fluid exerts on an object perpendicular to the ﬂow direction. — Drag is due to pressure forces and viscous (friction) forces. — Consider a flat plate (1) aligned with the flow; (2) angled with the flow; (3) perpendicular to the ﬂow. We have friction only; pressure and friction; and pressure only, respectively. —- Pressure drag also called form drag, and is due to ﬂow separation (which is caused by friction). Flow separation. Streamlines detatch from objects. — As ﬂow around oject velocity: low then high, then low; pressure: high then low then high. Bernoulli equation relates pressure and velocity. * Friction causes a loss in pressure so P cannot recover fully and the flow separates, leaving a low pressure wake behind the object. — This is counteracted by streamlining, to avoid separation. * Reduces pressure (form) drag, but increases friction drag. * At high velocities, pressure drag dominates over friction drag. — SEE FIGURES ON PPT SLIDES Drag Coefficients — Recall: f = 75217—2. — NOW: CD = Tifm. * A is the frontal projected area (or sometimes the plan-view projection, e.g., wings). * Usually combine effects of pressure and friction. e Spheres: * Low Re (up to 3) Stokes law: CD = 24/Re. * Higher Re requires correlations: see Table 11-2, Figs, 11—34, 11—36. ~ Other shapes in Table 11—1, 11—2. — Flat Plates: =o< Critical Re between laminar and turbulent is 5 X 105. * Laminar: CD = 1.33/Rel/2. * Turbulent: CD = 0.074/Re1/5. * Laminar and Turbulent on one plate (in the turbulent region): CD = 0.074/R81/5 — 1742/Re. * See correlation for rough plates. 0 Terminal Velocity Example — Balance weight, buoyancy, and drag force. ~ Drag force depends on velocity: FD = %W2ACD. — Iteration required since CD = OD(Re). LEL-‘FW 1"[' ~— ExhonaJ Flag; “ﬂamwmmwuga "‘1' 1'“ Tex-1'. HQ I Ham, Ln 77/73 I I v "(mum-«4!, ax 'TD-ktwwaw) UPDJM7 z/éy‘ﬁﬁ I (sparkle, F’a} wt)“ ’ A #0 QW+A¥~ awvv wu {v Deimw‘n-r neéJ/u! "-“PW/‘ulf { bra], Hm Lav/H. bfggma {x-Li'r’x‘u/ //¢.o; A») T331 «2 Formal) I I ,W_~.. ._. M ' Exk/Muj Plan-7% m '71-“ 91’795')’ 3’ :n4ﬁﬁna” ’ 1M4“) 7’ (Mr-4'7 ,4,» in t has J “and; H's» MW ,7 " F’9U} (fl-1M M53? ’5 MW»! M "L Q "‘ ‘5"; 00 V‘) 'YH‘ QM [Ir straw up,“ ’51"/. , Exampiao g . Dfa; an Gay-Gr 57 .. 'T’rcoa éu,‘/v'»'w;ﬁ/ M}, Punk‘t/go . A‘ﬁthyv‘é mic; Lrw Kﬁ/ Dbj(£4_:ffmim U»c’ms-}v-J «J 1" 05!’ 1"” Ora? do?!“ 0. adj-Eric Cord-(Pt); ‘_ 4 L4,- ‘ L‘M"““"7 /{-7Lu/J W . 1354'!) r 014de glwpm. D(;<U (id'ép . F712“) (2“ PM‘I};W. M 71’" 6J7]! a. (V6373; cm a” 4494/ J, £9 TL»: ﬂﬂg ’}>;mc./)m‘ D08 Me ‘3)“: {a CD "PM/MW ion,“ ..__‘7 waall {a L”; @ V§\$com ﬁngm| k1, Fahd] ~62 Snafu “‘4; :79 a. of n. J 6(¢_r) __,_ ,, c, A m“! T 7mm)- 791W W, 1.5, ‘D W ,LD éaPeHQJur— QFM a." 1‘ 0"”— Flak) v.5; sygow‘...“ ‘rMJ ¢—..a PM“ émet-"'M '47 Q’t‘w’f'“ Walk/t4 11w 714 nip)“ng Ecol! "’9 Efoﬁf’l’ ' CM wave) w/W’ '— W A W M W W m 37. 261% _./'\-— __._, v 5 “Raw 5 ‘ Fla-«3 61F. ﬁclauJ/f f“ ’4‘?!“ m“? Java, 7 {NJ/'69 [op all [MA—Q;- awake! ) Dam ‘p’h’tm—n WV"; ’ ﬂfrﬂL-A 5"“ QM" léssw poo \$9? ;s 73%; to /fi¢}£o--~. ..E;:”;ZI:,T”"7 9W” A9 51/0“) W m?“ sp‘w Shcnwlrm 7?}, (last {oi-PM} \M/oa'y’y Incl/(.444 - "rt—UM: % 4% 4"" Chi-wt”. + P \l?_ % f’vivé " [35}? “FHA. £7~1 ,u—v, w say-mm s7 ammzw- ‘ Red...“ T!» (MQa’H‘M. “4% . RECIth £07“ bf“? (?l(mr baa-7 3 _ W ﬁnk-Jim wk.) 7 " Imam. . é’l’lﬂdn‘vq‘a QMB 6rcﬂ*” g{ ww ~Do-fAutgi é», [Ag/cw D“; a; In“) g?“ch LIL“: )ovJ) ‘9, 4%. D3 éemocwt A. “I... E”*“‘”” 5/“) | CD ' C» (12!, PEP“ “’1. Fr 1 f D) \J) ﬂ/ 6 é PM’M 3 Dim/5 '3 éfwﬁ’i MP, 951i HEM W"? FD, f, L, v, ﬂ, .5 D “’7 \$0” m7, 4,7 w:th .p' 4? 3 *1" 0? VD. A? 1> 0‘ “ ' M‘ AP VJa-MMT r“, 7. fut/L L C v Z a7 4, : FD - ’ 4 .TZWUA I“? C, ; (1,747., 1,5110] 121 7 10 Chemical Engineering 374 Fluid Mechanics Fall 201 1 External Flows gBYU' IIKHKID [ Hum ‘\r “Ill Hm! rmﬂn’urul I-' .1 mi" :1 Ill) ‘.1 0| w r mum mm um [L] 1.0 in mi) moo lnmuIIX),(l1)0|l,llm,0(H) l'unn-lv le-inulxls munlx‘r hﬂl'p “=1” For mitigation of vortex—shedding induced vibration : Eliminates cross-wind vibration, but increases drag coefﬁcient and along—wind vibration t j ‘ Helical strakes _. 1/ ...
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## 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.

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Lecture_29_notes - ChE 374~Lecture 29—External...

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