Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 21 page Class Notes was uploaded by Jolie Shields on Saturday September 19, 2015. The Class Notes belongs to CE 321 at Michigan State University taught by Roger Wallace in Fall. Since its upload, it has received 43 views. For similar materials see /class/207369/ce-321-michigan-state-university in Civil Engineering at Michigan State University.
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Date Created: 09/19/15
Lecture 13 Newton s Second Law Linear Momentum Equation Aim To compute forces exerted by moving fluids on objects Momentum Momentum mass x velocity Mass 2 pdV Momentum pdVV Momentum U1 Lhc UllLllU system IVpdV lt6 J4 v4 w 2 j Vpdv ZFW 39T If vk DI Sys 41 Rate of change of momentum of the system sum of forces M Momentum Equation Reynolds Transport Theorem Coincident 17 control vulumc quot 77quot 77 7 2 J 2 J Z VoutpoutAoutIout Z IinpinAjnIin DZ 335 at cv Momentum Equation 2 Dr I 2 g I ZvoutpoutAoutVout Z sys 6 a I Z VoutpoutAoutVout Z ZFcontenlts olfthe cv contro V0 ume For steady ows 2 VoutpoutAoutVout Z in Am Z Z Fcontents of the control volume Derivation of the Linear Momentum Equation 7quotszsz ulpAlVl ZFx Time rate of change of vaAZVZ vlpAlVl ZFy the linear momentum of the system sum of Vuivj external forces acting on the system ma2F m2u2m1u1ZFx 1 V TV m2V2 m1v1 ZFy How to solve problems involving the concept of Linear Momentum Identify the control volume carefully Momentum can be positive or negative Forces acting on the control volume can be positive or negative Write the momentum balance equations in the appropriate directions xy for example Use the continuity V1A1V2A2 and the Bernoulli equations Problem 515 515 Exhaust assumed to have the properties of stan dard air leaves the 4ft diameter chimney shown in Video V53 and Fig P515 with a speed of 6 fts Because of the wind after a few diameters downstream the exhaust ows in a horizontal direction with the speed of the wind 15 NS Determine the horizontal component of the force that the blowing wind puts on the exhaust gases 15 ill 515 solution L szsz u1pA1V1 Z ZFx V2PA2V2 V1PA1V1 Z ZFy Vuivj 515 solution For he cam rol volume I39miam ed 70 X cmzpone 0f 7 momenim equafm is uleliz upV4 2 i where 140 uzsv TIMs V2 9 V2 14 A J Wane RX 139 Me Ile bar200154 Force Mai file MM ozr 00 7 09 exIam 70 TM 0 r01 14 Werehfp zif em Le rhlrhzgt 0r M1 000238 277Z4f1 15 O77 54515 Hence Fix units Rx 077 5 5g 26 21412 ProblemZ Determine the magnitude and direction of the x and y components of the anchoring force required to hold in place the horizontal 180 elbow and nozzle combination shown in Fig Neglect gravity 6 In Sccllon l p A 15 pg Iquot 5 ms solution slc39tio39n lt1 solution For deferm39mhj 7 X and y a lrec 39on CompanemJ39 of 1 endow forte 0 Cam m vaume r haz con71 1 e aw naye and mic Iaeweam fecr v39an 4nd 2 5 used 7718 com ra vanme and e gme Mumveal are ltawh 1h 15 Shhl Appim bn of 7 11 1 dPec on componen of 7 Mam momem um qua an 57 517 feed h 730 w solution HPlul om ml 145 Xdl rec ah Mpo mml 3974 7 3 quotHaw maMenrlum Egum 39on yields 4 Maul8 LIZ0141242 I XEAL I Fram he mservah39an of mass Eiu fan r9 pug1 pal12 2 Wm may be expressed as 0M1A1 7 PIAlv iixhlF AZ solution 7 1 F JMIA39MIML AIZHZ ou7 7l 4uzg 72 0 AZ 4x A56 14M 5 D u I11 1 1 AZ 91 39 muf D7 1 D1 7 1r ix nial xiiulp ulf7l T 1 7 I roz f 9 14 51 I In 5 125 2 l 144139 f 15 IL I lb 7T 2an 6m 5 a a H1 Slur n1 7 F M70 6 AX J 517 Water ows as two free jets from the tee attached to the pipe shown in Fig P5J7 The exit speed is 15 ms If viscous effects and gravity are negligible determine the x and y components of the force that the pipe exerts on the tee FIGURE P5 For he x comloonemL 01 2 re exequ by he pl pe On Me 66 We use Me 2 campanen f of The near marrien xm egaa Harv WW l o quot I7A r 22f F ayez Al 57a 4716 gtA3 1751 43 FX 5 A F I X 9 7 7 7e 17 we 35 cgn5ervav l39an 014 mas Q 239 Q1 f a3 w Avg9113 74513 a VI zvzj ay 23mlIsm4 asers m lz mg mquot39 l we we 39rnaui r egua m v w kw ManoZ f0 le fmaE PI it 7 L z 1 Em 779 lw IV F1345 39 40 5 001 In NM min 530 We 57 1 62 2 WM 52979fquot5 4500 L1n1 Fx W 72 0MN It pl 50 5 m e For My amW Mh 14m extMed i zJakohh 1 66 MIN56 y nu MGM 0 I N Mew mmm m era7 4 74 VZFVI 142 3 1551119993 I5g03m1 gecom f Fy Problem 529 Two water jets of equal size and speed strike each other as shown in Fig Determine the speed V and di rection 9 of the resulting combined jet Gravity is negligible v1o m Fov HW conhml volume shown 1n HIt Skeloty alcove nc Unear mamagm equa rion For he x and ydxm 39ans ave For Hm x AtrcL39HM VIQVLA1VCDSGDQVA o I and w H1 1 dtr chbn V ltV A stnefVA 0 2 Also Fm39 conservc ion 0F was we have PVIAI quot39 PV39LAI quot 9quotquot o 3 From Es1and 7 we qe V253 L56 09 If h SM 9 1 0 l 1 I OH erco Vzhoo l siwr 1 45 WA w H n 01
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