me106_s11 - ME-106 FLUID MECHANICS Spring 2011 O. Sava s...

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ME-106 FLUID MECHANICS Spring 2011 ¨ O. Sava¸ s Department of Mechanical Engineering University of California at Berkeley c ± January 11, 2011
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Preface These skeletal notes are meant to be a record of what was covered in class. ¨ O. S. Cover Photos: Top A Karman Vortex Street in the wake of Beerenber volcano on Jan Mayen island, June 6, 2001 Image courtesy NASA/GSFC/LaRC/JPL, MISR Team http://earthobservatory.nasa.gov/IOTD/view.php?id=2270 Bottom Smoke wire visualization of the flow past a semi-cylinder in wind tunnel. ME-107B, Sp03-Group T4 i
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Contents 1L e c t u r e - 1 1 1 .1 In t rodu c t ion . ....................................... 1 1 .1 .1 No ta t ion. ...................................... 1 1 .2 Con s t i tu t iv er e la t ............................... 1 1.1.3 Compressibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 .4 Su r fa c et en s .................................. 2 1 .2 Th r e ev i lflu id s...................................... 3 1 .3 K i t ch enexp e r im t s .................................... 3 2L e c t u r e - 2 4 2 .1 F lu ids t i c s-1. 4 2 .1 P r e s su r ea tapo in t................................. 4 2 .2 Cau chy st e t rah ed ron . .............................. 5 2 .3 F t i c sequa t 5 3L e c t u r e - 3 6 3 t i c s-2. 6 3 t i c t ion-r ig idbodymo t ................... 6 3 .2 U - tub emanom e t e r................................. 6 3 .3 Th tmo sph e r e .................................. 6 3 .4 S tanda rda e r e ............................... 7 4L e c t u r e - 4 8 4 t i c s-3. 8 4 idinr idbodyro t ........................... 8 4 .2 S t i cfo r c eonsu r c e s .............................. 8 4 .3 Buoy an cy . ..................................... 8 4 .2 En e rgyequa t ion :B e rnou l l iequa t ion-1 . ........................ 9 4 .2 .1 En e rgyEqua t ................................. 9 4 .2 In comp r e s s ib l eflow. ................................ 9 ii
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5L e c t u r e - 5 10 5 .1 En e rgyequa t ion :B e rnou l l iequa t ion-2 . ........................ 10 5 .1 .1 Comp r e s s ib l eflow . ................................ 6L e c t u r e - 6 11 6 .0 .2 Examp l e :Pun c tu r edt i r e ............................. 11 6 .1 Eu l e r sEqua t ion . ..................................... 6 .2 F lowexamp l e s–1 . .................................... 12 6 .2 .1 R ig idbodyro ta t ............................... 6 .2 L in ev o r t ex . 7L e c t u r e - 7 13 7 .1 F l e s–2 . 14 7 .1 V i s cou sv o r t .................................. 7 .2 P i to t - s t i ctub e .................................. 7.1.3 Uniform flow: u =( U, 0 ).............................. 8L e c t u r e - 8 15 8 .1 Cou e t t eflow. ........................................ 15 8 am ina rP ip eF low. 16 9L e c t u r e - 9 17 9 lowK ema t i c s ...................................... 17 9 .1 S t r eam l e s ,P a th l e s ,S t r eak l e s ........................ 9 .2 S t r l e/P a l eexamp l e :S tagna t ionpo tflow . ................. 18 10 Lecture-10 20 10.1 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 11 Lecture-11 22 .1Con s e rv a t ionEqua t s-I . 22 12 Lecture-12 24 s e a t t s-I I ................................ 24 .1Ma s sCon s e a t ion. iii
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13 Lecture-13 26 13 .1Con s e rv a t ionEqua t ion s-I I I ............................... 26 .1 .1Mom en tumCon s e a t ion . ............................ .2BodyF o r c e s..................................... .3Su r fa c eF o r c e s ................................... .4T o ta lF o r c e 14 Lecture-14 27 14 s e a t t s-IV. ............................... 27 15 Lecture-15 28 15 .0 .1En e rgyCon s e a t ion. 28 .2S t eadyS t r eamT ub low. 16 Lecture-16: Mid Term Exam 1 30 17 Lecture-17 31 17 .1Exam -1d i s t r ibu t ed. .................................... 31 .2D e r t ia lflowana ly s i s.................................. 18 Lecture-18 33 18.1 Mass conservation for an in²nitesimal element . . . . . . . . . . . . . . . . . . . . . . 33 18 .1Ca r t e s iancoo rd ina t e s ............................... 33 19 Lecture-19 35 19 .2Cy l ind r i ca lcoo t e s .............................. 35 .1D e r t s i s-1. .1S t r eam fun c t .................................. .2Examp l e s ...................................... 20 Lecture-20 37 20 e r t s i s-2. 37 .1l in ea rex t s ionra t e ................................ .2d i la t t e ................................... .3s t ra inra t e...................................... iv
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20 .1 .4ro ta t ion-v o r t i c i ty. ................................ 37 .5po t en t ia lfun c t ion/po t t lflow . ....................... 21 Lecture-21 38 21 .1D iF e r t lflowana ly s i s.................................. 38 .1Un i fo rmflow . ................................... .22DSou r c e...................................... .3V o r t ex. ....................................... .2Comp l expo t t lflow s .................................. 39 .2 i rmflow+Sou r c e+V o r t ........................ .22DD ipo l .3Un i rmflow+D l e :flowpa s tcy l ind e r....................
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This note was uploaded on 01/28/2011 for the course ME 106 taught by Professor Morris during the Spring '08 term at University of California, Berkeley.

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me106_s11 - ME-106 FLUID MECHANICS Spring 2011 O. Sava s...

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