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Lecture_6_notes

# Lecture_6_notes - ChE 37 4—Lecture 6—Mass Balance 0...

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Unformatted text preview: ChE 37 4—Lecture 6—Mass Balance 0 Reynolds Transport Theorem: 5351.15— : % pde + fA pbl? - FidA. pbi? - FL is the ﬂux of B stuff through the control surface. 0 Integral Mass Balance 1. B = 1W, b=B/ZW= 1. 2. Apply the conservation law: (11W / dt = 0: mass is conserved. 3. 3% fCV pdV + IA p17~ ﬁdA = 0. 0 Cases 1. Steady State 2. Constant density * Liquids have approximately constant density * Gas density: ideal gas law: vary pressure (high speed ﬂows or compressor), vary temperature (e.g., combustion)7 vary moles (e.g., combustion/ reaction). 3. Uniform inside C.V. and/ or Uniform inlet / outlet flows over surface. 4. Fixed or variable C.V. The control volume C.V. can move —; * v : Usys ‘ ’Umr * Can pull the d/dt inside the integral. (id—I? : min _ moat 0 Examples 7 Simple flow with change in area of inlet / outlet. * Fixed CV, SS, Constant ,0, Uniform Flows. — Filling a tank with inlet and outlet. * Constant ,0, Uniform Flows. not SS, none-ﬁxed C.V. — Nonuniform flow —> compute the average velocity from a velocity proﬁle. 0 Differential Form of Mass Balance. — Get from the Integral form with a small/ uniform property control volume and shrink to a point. — Get from the Gauss Divergence Theorem. élaeg é, — 33%er r1455 Batch/\th ‘- ABS)’; 1’75] At :ﬂ/W + X PEUYA‘CJA CV £3 CD rszr’) (#10 H, i: i fﬂf & 8/0333" L ' E“ ~l At Jt eﬁ" cu (,5 C7; Come/Na; am {W M“ WWW“H L Q in: .... rpm J'gon/SJA -.~ A O \iLELMW as W mﬁ N)! @603 cl "" > :: A g ‘ L;‘I,‘- fay Lowe}, K/af‘) "5 {‘99 A . :3.“ : MM ' Mod 71/ /" Cw CAaTz q bu f— Exnmfk ! @ M— 043“, 3.5-. ...__.. @J :27“) cu. ——- Y Q? éoM'i f’ --> Y Q: Uhvl‘p {n/QJ ———‘> m \JLAL : \J.A' “WWW” MW” 0’ 00M”, =(f’m0L _’§ _ ' V1 7. \)‘ A. 1 m .7-1 ’ Mom} ._. ’21.“ z ' A}, 1 ﬁg}. At Dar? ﬂ 4'2; 7; + VLAI "va; :0 [LS t Atk ’ Q m A—(, )7th 3—1:: - M.'01AL A—L L/ﬂwnw (and (_ \$0M “>- LL : Lo + (mmvuwaf ‘ At M4124 In on? W 59h: pm; ' I {a Sr to (9 ‘Plug H1 éfum VCx')’ £64 JA 1 gwk 4,9 4,}: LAC/Ix ‘ In‘hafJVt. ___—___'______________ D; :4 Mac’g EJ‘ “(1 K “WWW” ‘11 x‘7 7171, nyd L,Ul I L94 farm u A” u i ’9‘ by “*1” v} to AK (V a: 7‘./. x17. J V‘ "2;; - x L 0H: fluib)’ f'U'Ay 4 auIAx - WV‘AK =0 Axbw/ Luz“ AMA/9 MA AX, ()7 1007 & lat-«Iv, A? “W I a f )‘778‘ “TAXHAV —-—w- f ; luv/D“ :7; " M "’ ’+ 2.315;”: ‘lwx Ax ny-‘Do ~——> 9)” by ._..~— Jr 91”“ '2»? "wk :1: + --"*U :0 '37 (‘9 “5 J + v F3 :01 “3+ -—> C) ‘3 '_I ~— NM’U *SNW-(NM’U ~O mmmm. a’i A.» gag??? 4 v. A '2] 12.6) 2 Qf’ ~3- p“- + Volp‘v ...
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Lecture_6_notes - ChE 37 4—Lecture 6—Mass Balance 0...

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