Frqvw iw z y7 3 3 ru oltxlg phwkdqro iurp

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Unformatted text preview:  ) 6RQQWDJ %RUJQDNNH DQG YDQ :\OHQ 9ROXPH ([SDQVLYLW\ DQG &RPSUHVVLELOLW\ ( 'HWHUPLQH WKH YROXPH H[SDQVLYLW\ α3 DQG WKH LVRWKHUPDO FRPSUHVVLELOLW\ β7 :DWHU DW  )  OEILQ FRPSUHVVHG OLTXLG α3  ∂Y  ∆Y Y ∂7 3 ≈ Y ∆7 3   ) IRU ZDWHU DW  )  OEILQ DQG DW  )  OEILQ XVLQJ WKH VWHDP WDEOHV 8VLQJ YDOXHV DW  )  ) DQG  )       α3 ≈      β7  ∂Y  ∆Y  Y 7 ≈  Y 7 ∂3 ∆3 8VLQJ YDOXHV DW VDWXUDWLRQ  DQG  OEILQ       β7 ≈      LQOEI    :DWHU DW  )  OEILQ FRPSUHVVHG OLTXLG       α3 ≈            β7 ≈         )   LQOEI 6RQQWDJ %RUJQDNNH DQG YDQ :\OHQ ( $ F\OLQGHU ILWWHG ZLWK D SLVWRQ FRQWDLQV OLTXLG PHWKDQRO DW  )  OEILQ DQG YROXPH  IW 7KH SLVWRQ LV PRYHG FRPSUHVVLQJ WKH PHWKDQRO WR  OEILQ DW FRQVWDQW WHPSHUDWXUH &DOFXODWH WKH ZRUN UHTXLUHG IRU WKLV SURFHVV 7KH LVRWKHUPDO FRPSUHVVLELOLW\ RI OLTXLG PHWKDQRO DW  ) LV  × − LQOEI Z  ⌠ 3GY ⌡   ⌠ ∂Y G3 3 ⌡ ∂3 7 7 β7 ≈ FRQVW P  ×  ⌠ Yβ7 3G37 ⌡   )RU Y ≈ FRQVW  IW ! Z  Yβ7     3  3 )RU OLTXLG PHWKDQRO IURP 7DEOH )  ρ 9 :   OEP  OEPIW  ×  × 10−      ×  > @  IW OEI  %WX 6RQQWDJ %RUJQDNNH DQG YDQ :\OHQ ( 6RXQG ZDYHV SURSDJDWH WKURXJK D PHGLD DV SUHVVXUH ZDYHV WKDW FDXVHV WKH PHGLD WR JR WKURXJK LVHQWURSLF FRPSUHVVLRQ DQG H[SDQVLRQ SURFHVVHV 7KH VSHHG RI VRXQG F LV GHILQHG E\ F = ∂3∂ρ V DQG LW FDQ EH UHODWHG WR WKH DGLDEDWLF FRPSUHVVLELOLW\ ZKLFK IRU OLTXLG HWKDQRO DW  ) LV  ×  LQOEI )LQG WKH VSHHG RI VRXQG DW WKLV WHPSHUDWXUH F ∂3 V ∂ρ Y ∂3 V ∂Y   ∂Y Y ρ ∂3 V ρ  βVρ )URP 7DEOH ) IRU HWKDQRO ⇒F  × ××     OEPIW  IWV 6RQQWDJ %RUJQDNNH DQG YDQ :\OHQ ( &RQVLGHU WKH VSHHG RI VRXQG DV GHILQHG LQ 3UREOHP  &DOFXODWH WKH VSHHG RI VRXQG IRU OLTXLG ZDWHU DW  )  OEILQ DQG IRU ZDWHU YDSRU DW  )  OEILQ XVLQJ WKH VWHDP WDEOHV )URP SUREOHP   F ∂3 V ∂ρ 7 Y ∂3 V ∂Y /LTXLG ZDWHU DW  )  OEILQ $VVXPH ∂3 V ≈ ∆3 ∂Y ∆Y  8VLQJ VDWXUDWHG OLTXLG DW  ) DQG FRPSUHVVHG OLTXLG DW  )  OEILQ F F    ××   Y  IWOEP V V V  %WXOEP 5  ) Y  ) Y ×  IWV 6XSHUKHDWHG YDSRU ZDWHU DW  )  OEILQ $W 3 $W 3 F F  OEILQ  OEILQ     IWV  7  7  IWOEP  IWOEP  ××   ×  6RQQWDJ...
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This note was uploaded on 10/28/2009 for the course ME 2103241 taught by Professor Jtt during the Spring '09 term at Chulalongkorn University.

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