Lecture_25_notes - ChE 374—Lecture 25—Integral Momentum...

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Unformatted text preview: ChE 374—Lecture 25—Integral Momentum Balance 0 Integral Momentum Balance — Find Forces or Accelerations . 213 : %fovp17dV-l- fOSpJU-fi’d/l. — For uniform properties: Xi“ = aw?) + (2W? 0... — (2W7 m — For uniform properties and Steady State: 2E = (; mam M (2 me in >l< TAKE THIS EQUATION LITERALLY. - Vector components are positive in the positive coordinate direction. - m = pAl'UI is a scalar quantity, always positive. — Note: m6 is momentum flow rate. — Note: p171? is momentum flux. — Note: poser—f is x—momentum flux. 0 Choose a control volume — Not limited to the fluid — Choose it perpendicular to inlets and outlets — The momentum balance is WITH RESPECT TO THIS CV. * So velocities are RELATIVE to the control volume. * Also, 7%; is also relative to the control volume. 0 Forces are (1) BODY; (2) SURFACE; (3) OTHER — Body forces are gravity (mg). — Surface forces are Pressure (always normal to CV, and towards the CV); and viscous forces (usually neglect at inlets and outlets where the flows often cross the boundary) — Other forces are external, like bolts, the ground, and other anchoring forces, etc. o Momentum flux correction factor corrects for nonuniform flow at inlets and outlets. Similar to kinetic energy correction factor. ,8? % fv2dA. ,6 : 4/3 for laminar a? % f'usdA. a : 2 for laminar 0 Example: Flow through a nozzle. — Restraining force is F = A1(P1 + pu§(1 — Al/Ag), where (1) is inlet, (2) is outlet, and F is in the direction opposite the flow. 0 Example: Flow deflected 90 degrees: — Restraining force is F = 7m}, with force directed opposite the flow. 0 Example: Flow deflected 180 degrees: e Restraining force is F 2 2m, with force directed opposite the flow. 0 Example: Flow deflected 6 < 90 degrees: F1 2 inv(1 * cos 0), x is flow inlet direction, and FI is opposite the flow direction. F,, = mv(sin 6), y is perpendicular to inlet direction, and Fy is with the direction of deflection. 7% XXL.ch M1 >56 7 ‘Plu\e’ §{-a416§ ' Wag ROLa/M( true/777 gala—wt Xg mantwfl‘w 'Ealflmcf CLP "l (bch r1amon¢v~> \léloolxl/ T’TO'QI'IUA aw" Foffcs ,——-_». ,Vtow,’ F ': M (L '; MJU ’ ;: ' : I7.o}f 0Q IflDMt‘A7me' D‘C/N‘Jt’fj Lav/Jam PIP? UleC“!'/ “'3'!” , 4 F076! (MOMCwJ'VV‘) 734mg “ Use) a Difiozm‘p‘ol APV(ML_ * — 0wa; DO low-{'6 {4’ APP/oku 71‘0" fiv‘gcm (($55) Dch/uwflo' Kola;ch {imman/ 600‘ (:04; F) 0- ’ (a él‘OO‘A #mcw I tr! .3 I 6‘}C ' f/f‘ RCYnoU5 5T}a"9fw)% 2E5” : lgfbév 4 g (“9'0 13A J E:M‘\J}, 13:?) 7? “L s W A F; DIF F a ’M’ as Uw-‘wax FWWH’C’” ’1‘ , a ~ + (757 -( Mg). , f MV _,, ow} 2: n’\ N M ( 3 Kid/V._____._—J .4 _, «4 A O a! §.§ (U kmls we? (Ulfvowf’vtfis ~ vmar F4 / 7 can .4» x, 7 QMPMML; N941, “)1 Q )3 Momw;v* )75‘46 .‘ Z I; Vol,qu '- \Qc’xk [MPHCH 71-.- kg( or a. , Vclacfhw at? gala-hut {a a“, fi \) f v ,. v_ Va", ’ Bf ‘. f ’@ r V « ’—>> @9H‘t/7 CPD» Viva 7L: 'Ddzw‘l; )Mv‘Jr $3...) my» aaon 76.” a” 9mm 0? 7“ «Wk, my, M LIMCJV) ‘éhooér m1, _L to amid/MM. V C. .V, ’l‘ml‘¥<’3 ({D F’L—u‘CJ ' In 6) I &»’1}—/ 11M “0"{2070 Xv chC/g {’1 71w §L\“Jc<) 41762 I‘M‘ ‘— }(_ luv-x « Tqu can ‘€/<+Cflno)l Fact/J ExamPlt I Flak: {Lrwak Na'ulf "fl. 8. 7; . ping Fm“ of. TsoHs, * 6516.“ (a) \J‘IAUAII éouCD/lfnj I i ) v. I ’ _.\ ' PA ’ r — — , 'i ( "L [M‘Jld * («wk I) t VJ) z/oAlUl F0366(WVOW\ bfafilowx limrcs ¥ra- Fl 30H; 25’ “Z’VL A(fi,fim ‘ 45—... fi' \ ( l"9 “LAmj‘P/HZKQ)‘: ’VDAN} - m, :lel as : 'Ely'Al + 79A”)? “‘ PA‘L (gi/A') A if F5- AI?) +fv'1(‘~fij] ' Flo“) have , ‘ an! (now/“3 Foec X' D‘ftcya“ ‘" A+~\ (flank rJh *4 \ v—a ’5,“ : "’l’vl X " mom‘cu'hdm ', *F .: y:/1 e .__. M V t "Nter 7\ \'M0M(¢\+W\ ; -1 , ~ - MM F / — W \J 949 Thus'kg x F”: MU([—'(¢Jfier) Tfy jg F7 :- M \JS‘I'flC—D '2‘ ___, w—b s ——L I0 : Irx‘t 4 r7] LN . ND+¢ éOu'tI 14M vx)(I'H'5.,\ x_ M .. %_7;\)¢0$Q ——-—> Fx -—)>. Fx : M (059 _ Mv J— » é \ i —> C brad rx I 4" 6’71 1*“?!ch (\- mk a 3‘ I; E M €7vx / . . 1-) : 3—? Fx #9 I a”) {2’7" IMP’DC’] F», 71%“ 6 )K A f n I; #9.. 7 99 7'3: ‘J m(4v) ‘6‘“) fl“? X-“p’1/7 '1, #23 mi 6; ' 65‘ T3001: ' WI“ L! ur‘gjrz'ac’y? ’ BC 0‘44»? “90—3 iH+M,°rr,Lr‘7 Wr~;# M 330a};- éf—i + *1» Wk) 9 i , ‘7 a? a (W) Mm W .1“ H v I l 1" {S 71% Mtg/074412“ TQM, Dr“)? “’7 m 124% g WM” “Nam/c1), 0 KW “L94 {0 b0 If no? 0,.)Lgpury £3. ans) JnJ’7IQH f Z ‘SffiilUMcJA Q [.9 C ' . ...
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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_25_notes - ChE 374—Lecture 25—Integral Momentum...

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