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Lecture_13_notes

# Lecture_13_notes - ChE 374—Lecture 13—Mechanical Energy...

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Unformatted text preview: ChE 374—Lecture 13—Mechanical Energy Analysis of Steady Flow 0 Kinetic Energy Correction Factor — g term appears in energy equations — Usually assume uniform v. — In general 11 is nonuniform (e.g., pipes have v20 at the walls). * For mass ﬂow7 just use average velocity, then can treat as uniform. * For K.E. this does not work since '52 # 11—2 — Correct with a fudge factor, 0:: K.E. : @172. — a 2 2 for laminar flow and a = 1.04 — 1.11 for turbulent ﬂow. — Often ignored: * Most flows are turbulent * ICE. is small compared to AP, or A2. >I< Small error compared to other assumptions or unknowns. 0 Friction and Mechanical Energy Losses — SS Energy Equation: . . AP A2 Q+W5=mAu+m<T+Tv+9Az). W Aemech — We’ve been ignoring Q, W5, Au. — Now, account for W5 and “Losses”. — Observations: 1 Take 2 W5 = Au 2 0 —> Aemec;Z = 0 —> emech is conserved. 2 Consider a heated pipe, no friction, then mAu : - So that heat a Au 3 Friction converts mechanical energy to internal energy. - Au not from heat transfer is from friction losses. Rearrange Energy Eqn: - F is +. ~ F decreases emech. - Book calls this Emech,loss~ 4 Head Form: AP A212 ——+—+Az=hw—hL pg 29 - with hL = F/Thg, hw = W's/nag. - Normally F is friction in pipes, with losses in pumps accounted with efﬁciency. o Examples: e Example 1: Raise a liquid: hm : A2 + hL. — Example 2: Pump a liquid: hw 2 Ap—f + hL. . T _ AP _ A 2 _ Example 3. Nozzle. —E A 2”; + hL. — In each case, hL is wasted: Az, AP, and Av are less than without loss. ~ Text 5-94. 0 Note: one equation, one unknown: (m, AP, A112, Az, W3, 77, — Set all but one and solve for that one. CONSIDER THIS IN BOOK EXAMPLES, HW. Laban (K —- ['Vlfctaa’s/CCJ‘ Eat/k Wu l‘lfM 7 (last, PIE/0.33:4 {4.2. ColluL‘o-a Qua 0L Fw'dim/ Lacs K . LE. Lv(f¢¢+iov\ Qndmﬁ "L \l W TMM :1 (Mg 1 r? Anﬁlﬁr'g Q‘P \$4654 F (on! " 01: V35 t AU :0 p“? 1.5-6.4 to M €M coﬂsﬁn‘s") ' \ .E. 2. H6640? 7 no [#:45er I \ . . M—3‘ 1 AM = a New! ->> Au. ’5. Fﬁ-C'b'oﬁ Camuw+9 Meckaar'cq! Cmmiy b ,‘zw’mﬂa ' {AWLﬂi/ 1—3” “8* f0“ ﬂaw/b) I”; / 12'th L049 /‘ + gm '7 \;)S 4 f9 "L W .E/ig-f— #7 Dedle em Eyck (all/J EMC‘L‘I Less. 4 H648 Fol“: A? ’7‘ r ‘ 7g 4 1:37— 4 A? r Ll.) ’ LN, LL : ’27 .144 (:{DL/ LL FCF‘J PDM {p oQC’N-‘ﬂ( 1’" I ¢ ry‘Je {;‘ 1 3 k . 7 MW 5, cc. Us. , ﬂ.» . a; “saw «L» raw ‘ ” aw ‘ ‘ r 1 s W r; P Q \ _ \L J, .0- 1.. w { % + : a1) -" r’) J / ‘ 'PI'LL 1 Pang); : » mi‘fk ‘43s, F 71"“ (“Dag-Maw HRH” , 60 \3/ 7L4 New ’ “)5 PM em “’7 ’2," {g M I 6196 7"J “W”? “*7” ' é‘wvb'ﬁ/ 2 \1. : \Jq a) P, = P1 (Pdw A Q37 1: ': . H4204 Fo/ﬁx ‘1' 1 Q 1‘ .3 5. 1 a) Q (h s... 1 TQM f4) ' (gm.'g\\,«/F,L3>(L'LI‘H3Z{") ; 7”f,7é"o»«/5 J 1 317 «Pl/£1- w 315.2,... f “Pow? : "’7le z / H7 @ . Ma'kZVBC (MN m alfﬂéo (an ,ab,“ PM Praia m LIL-r TM. ' 0% vim Anya»? 6901“ maﬁa/w, Naif Lou-J {o (0.4m) ’60ka \Aﬁﬂ'J [aha/4. ...
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