Tarea Final Mecanica de Fluidos

March 25, 2018 | Author: Marcela Valencia | Category: Pressure, Viscosity, Pump, Friction, Gases
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ͺଶ ሺͲǤ͵͸ଶ െ ͲǤͳͺଶ ሻ ͳͻǤ͸

ࢠ૚ െ ࢠ૛ ൌ ૙Ǥ ૜૚ૠc

c ¸   $   % % 

ࢠ૚ ൅ ࢠ૛ ൌ ૙Ǥ ૜૟c

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ߩଶ ൌ

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ܲଶ ʹͲͲ‫Ͳͳݔܽܲܭ‬ଷ ൌ ൌ ૛Ǥ ૙૟࢑ࢍȀ࢓૜c ܴܶ ʹ͸Ͳሺ͵͹͵Ǥͳͷሻ

.3 %   $ 

Ͳ ൌ ݉ሶ ଵ ൅ ݉ଶ െሶ ݉ሶ ଷ 

ܸଷ ൌ

ߩଵ ܸଵ ଵ ൅ ߩଶ ܸଶ ଶ  ߩଷ ଷ

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c c c c c cc c c cc cc cc c cc c   



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ܸଵ ൌ

— %@

ܸଵ ଵ ൌ ௕ ܷ௕ 

௕ ܷ௕ ͳͲͲ ଶ ൰ ܷ௕  ൌ൬ ଵ ͷͲ ܸଵ ൌ

ܷ௕  Ͷ

ܲଵ ܸଵ ଶ ܲ஻ ܷ஻ ଶ ൅ ൅ ܼ஻ ൌ ൅ ൅ ܼଵ ൅ ݄௖  ߛ ʹ݃ ߛ ʹ݃

ܲ஻ ܷ஻ ଶ ܲଵ ሺͶܷ஻ ሻଶ ൅ ൅ ܼ஻ ൌ ൅ ൅ ܼଵ ൅ ݄௖  ߛ ߛ ʹ݃ ʹ݃ ܷ஻ ଶ ൌ

ܷ஻ ଶ ൌ

ʹ݃ ܲ஻ ൬ ൅ ܼ஻ െ ܼଵ െ ݄௖ ൰ ͳͷ ߛ

ʹ‫ͻݔ‬Ǥͺͳ ͷͲͲ ൬ ൅ Ͳ െ ͲǤͶ െ ʹǤͷ൰ ͻǤͺͳ ͳͷ ܷ௕ ൌ ͹ǤͻʹͻͲ݉Ȁ‫ݏ‬ ܸଵ ൌ ͵ͳǤ͹ͳ͹݉Ȁ‫ݏ‬

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ܴ௫ ൌ

ܴ௫ ൌ ܲ஻ ஻ െ ߩܸ஻ ଶ ஻ 

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)!  %! !  /     / Ÿ ൌ ʹͲͲ ൅

ͷͲͲͲ ‫ͻݔ‬ͺͳͲ ൌ ʹͶͻǤͲͷܰ ͳͲͲଷ

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ߨ ܴ௬ ൌ ͳͲͲͲ ቀ ‫Ͳݔ‬ǤͲͷଶ ‫ͳ͵ݔ‬Ǥ͹ͳ͹ଶ ቁ ൅ ʹͶͻǤͲͷ Ͷ ܴ௬ ൌ ʹʹʹͶǤʹ͸͵͹ܰ

          !              !   "  3 *  " 7   !  @ c Q  ൌ Q ࢞࢓ሶࢂ െ Q  ࢞࢓ሶࢂ ࢙



ò஻ െ ͲǤʹͷŸ ൌ ‫ܸߩݎ‬ଵ ଶ 

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c +c 

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    !     /      ݄௟ ൌ ʹǤͷ

ܸଶ ܸଶ ܸଶ ൅ ൌ ͵Ǥͷ  ʹ݃ ʹ݃ ʹ݃

2 $ ! " ! 

݄௧ ൌ ܼଵ െ ܼଶ െ ݄௟ 

݄௧ ൌ ͷͲ െ ͳͲ െ ͵Ǥͷ

ܸଶ  ʹ݃

݄௧ ൌ ͶͲ െ ͵Ǥͷ

ͺܳଶ   ߨ ଶ ݃«ସ

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c

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࢓૜ c ࢙

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ܸଷ ଷ ൌ ܸସ ସ ՜  ܸଷ ൌ ܸସ

ܸଷ ൌ ܸସ ൬ 

ସ  ଷ

«ସ ଶ ʹǤͷ ଶ ൰ ൌ ʹͲ ൬ ൰ ൌ ͳǤʹͷ݉Ȁ‫ݏ‬ «ଷ ͳͲ

  (! %    ܸ௦ ൌ ܸଷ ൬

«ଷ ଶ ͳͲ ଶ ൰ ൌ ͳǤʹͷ ൬ ൰ ൌ ͲǤͺ͸ͺ݉Ȁ‫ݏ‬ «௦ ͳʹ

   !    !    %  /  ! "   01*!     ܼଵ ൌ

ܲ௦ ܸ௦ଶ ൅ ൅ ܼ௦ ൅ ‫ܪ‬௟௦  ߛ ʹ݃

ܸ௦ଶ ܲ௦ ൌ ሺܼଵ െ ܼ௦ ሻ െ െ ‫ܪ‬௟௦  ʹ݃ ߛ

ܲ௦ ‫ܮ‬ ܸ௦ଶ ൬ͳ ൅ ݂ ൰ ൌ ሺܼଵ െ ܼ௦ ሻ െ ߛ « ʹ݃

ͲǤͺ͸ͺଶ ܲ௦ ʹǤͷ ൬ͳ ൅ ͲǤͲʹ‫ݔ‬ ൰ ൌ െͳǤͲͷͶ݉ܿܽ ൌ െͳ െ ͳͻǤ͸ʹ ߛ ͲǤͳʹ ܲ௦ ൌ െͳǤͲͷͶ‫ͻݔ‬Ǥͺͳ ൌ െͳͲǤ͵ͶͶ‫ܽܲܭ‬

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ܲௗ ܸସ ଶ െ ܸௗ ଶ ൌ ܼସ െ ܼௗ ൅ ݄௟ ൅  ߛ ʹ݃

ͳǤʹͷଶ ͳͲͲ ʹͲଶ െ ͳǤʹͷଶ ܲௗ ൌ ͸െͲ൅ ‫Ͳݔ‬ǤͲʹͷ‫ݔ‬ ൅  ʹ‫ͻݔ‬Ǥͺͳ ͲǤͳ ʹ‫ͻݔ‬Ǥͺͳ ߛ ܲௗ ൌ ʹͺǤʹͻ͹݉ܿܽ ՜  ܲௗ ൌ ʹ͹͹Ǥ͸ͳ‫ܽ ܭ‬ ߛ

      ! ! ! %  / !     *   ܲௗ ܸௗ ଶ ܲ௦ ܸ௦ ଶ ൅ ൅ ݄௕௨ ൌ ൅  ߛ ʹ݃ ߛ ʹ݃ ݄௕௨

ܲௗ ܲ௦ ܸௗ ଶ ܸ௦ ଶ ൌ െ ൅ െ  ߛ ߛ ʹ݃ ʹ݃

݄௕௨ ൌ ʹͺǤʹͻ͹͵ െ ሺെͳǤͲͷͶሻ ൅

ͳǤʹͷଶ െ ͲǤͺ͸ͺଶ  ͳͻǤ͸ʹ

݄௕௨ ൌ ʹͻǤ͵ͻ͵݉ܿܽ

! 7   ' "!   Ÿ௔ ൌ

ߛܳ‫ܪ‬஻ǡ௨  ߟ஻

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c c c c cc! c c cc c cc c  c  cc c

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—   "  37-  ՜ Q ‫ܨ‬௫ െ ݉ܽ ൌ Q ݉ሶܸ െ Q ݉ሶ ܸ௥  ௦



െ‫ܨ‬௙ െ ݉ܽ ൌ Ͳ െ ݉ሶܸ௥  ݉݃ߤ௞ ൅ ݉ܽ ൌ ݉ሶܸ௥ 

   *!   2!7݉ሶ



ሺ݉௢ െ ݉ሶ‫ݐ‬ሻ݃ߤ௞ ൅ ሺ݉௢ െ ݉ሶ‫ݐ‬ሻܽ ൌ ݉ሶܸ௥  ݉ሶ ൌ

݉௢ ሺ݃ߤ௞ ൅ ܽሻ  ܸ௥ ൅ ‫ݐ‬ሺ݃ߤ௞ ൅ ܽሻ

1c    4

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cc —       .!   "  ! $ > %9*ߩ

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    - ò௫ െ Ÿଷ ൬

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‫ܮ‬ଶ ‫ܮ‬ଶ ‫ܮ‬ଶ ‫ܮ‬ଶ ʹ‫ܮ‬ଶ ʹ‫ܮ‬ଶ ൅ ൰ െ Ÿସ െ Ÿହ െ Ÿ ‫ܮ‬ଶ ൌ ߩܸܳሺ ൅ ൅ ‫ܮ‬ଶ ሻ ͵ ͵ ͸ ͵ ͵ ͵ ò௫ ൌ ൬

Ÿଷ Ÿସ ʹŸହ ൅ ൅ ൅ Ÿ ൅ ʹߩܸܳ൰ ‫ܮ‬ଶ  ͵ ͵ ʹ

ò௬ ൅ Ÿଵ

‫ܮ‬ଵ ‫ܮ‬ଵ ‫ܮ‬ଵ ‫ܮ‬ଵ ൅ Ÿଶ ‫ܮ‬ଵ ൅ Ÿଷ ‫ܮ‬ଵ ൅ Ÿସ ൅ Ÿହ ൅ Ÿ ൬‫ܮ‬ଵ ൅ ൰ ൌ െߩܸܳሺʹ‫ܮ‬ଵ ሻ ʹ ʹ ʹ ʹ ò௬ ൌ െ ൬

    3

Ÿସ Ÿହ ͵Ÿ Ÿଵ ൅ Ÿଶ ൅ Ÿଷ ൅ ൅ ൅ ൅ ߩܸܳ൰ ‫ܮ‬ଵ  ʹ ʹ ʹ ʹ ò ൌ Ͳ

c  c)  3!         7L!   ! " 7 ! '7 



c c

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Ÿ ൌ ݂ሺ‫ܦ‬ǡ ‫ܮ‬ǡ ‫ܥ‬ǡ ߱ǡ ߤሻ

2 

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2 $ 

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ܰ ݂‫ݐ‬ ‫ͳݔ‬ ൌ ͹ͻ͸ͻ͸ܰȀ݉ ݈ܾ ͲǤ͵ͲͶͺ݉

2    ! $    

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‫ ܨ‬ൌ ͶͶͲ‫ିͲͳݔ‬ଷ ൬

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.'    "  3*!7 !  !  Ÿ ൌ ߛܸ௣ 

Ÿ ൌ ͹͸ͻ͸ͻ‫Ͳݔͳݔ‬ǤͶ‫Ͳݔ‬Ǥͳ ൌ ͵Ͳ͹ͺǤ͹͸ܰ 

‫ ߤܨ‬൅ Ÿܿ‫ݏ݋‬ሺ͸Ͳሻ െ ܶ ൌ Ͳ ‫ ߤܨ‬൅ Ÿܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܶ

ͶǤͶͲ ൅ ͵Ͳ͹ͺǤ͹͸ܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܶ      #  %    !  

Ÿ െ ܶ ൌ Ͳ ՜ Ÿ ൌ ܶ ܸ௚ ͳͳͶͲͲ ൌ ܶ

.  -! !   % 

ͶǤͶͲ ൅ ͵Ͳ͹ͺǤ͹͸ܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܸ௚ ͳͳͶͲͲ ܸ௚ ൌ ͲǤͳ͵ͷͶ݉ଷ 4: " 

  c $ "    !   "  3"  !$ K! $  ! 7 %    *$      $ ! (  3'! " "    !"  (  ! (-  



cc 2  ! ሺ݇ܲܽሻ  # *  *!  J!      ") ሺ‫݋݈݁݋‬ሻ  ሺ‫ ݏ‬ൌ ͲǤͺሻ.   !  ʹͲԨ*!   " ͹ͶͲ݉݉«݁‫݃ܪ‬Ǥ 

   c! !   % /   #     c   cc c (c "    (   !     (c %  !   ! !   c      !  3 (  # !   !  $ 7    ͲǤ͹ߛ௔௚௨௔ ൅ ͲǤ͵ߛ௛௚ െ ͲǤ͹ߛ௔௚௨௔ െ ͲǤͺ ‫ߛ כ ܵ כ‬௔௚௨௔ ൌ ܲ௔௜௥௘  ܲ௔௜௥௘ ൌ ͲǤ͵ ‫͵ͳ כ‬Ǥͷ͸ ‫ͻ כ‬Ǥ͹ͺͻ െ ͲǤͺ ‫Ͳ כ‬Ǥͺ ‫ͻ כ‬Ǥ͹ͺͻ ൌ ͵͵Ǥͷͷ͸͹‫ܽ ܭ‬ ܲ௔௧௠ ൌ ߩ ‫݄ כ ݃ כ‬

ܲ௔௧௠ ൌ ͳ͵ͷͷͲ ‫ͻ כ‬Ǥͺͳ ‫ כ‬͹ͶͲ ‫ିͲͳ כ‬ଷ ൌ ͻͺǤ͵͸‫ܽ ܭ‬

ܲ௔௕௦ ൌ  ܲ௠௔௡௢ ൅ ܲ௔௧௠ ൌ ͵͵Ǥͷͷ͸͹‫ ܽ ܭ‬൅ ͻͺǤ͵͸‫ ܽ ܭ‬ൌ ͳ͵ͳǤͻͳ͸͹‫ܽ ܭ‬  .' !   !  !  J 

ͲǤ͹ߛ௔௚௨௔ ൅ ͲǤ͵ߛ௛௚ െ ͲǤ͹ߛ௔௚௨௔ െ ͲǤͷ ‫ߛ כ ܵ כ‬௔௚௨௔ ൌ ܲ௠ 

ܲ௠ ൌ ͲǤ͵ ‫͵ͳ כ‬Ǥͷ͸ ‫ͻ כ‬Ǥ͹ͺͻ െ ͲǤͷ ‫Ͳ כ‬Ǥͺ ‫ͻ כ‬Ǥ͹ͺͻ ൌ ͵ͷǤͻͲ͸ͳ‫ܽ ܭ‬

ܲ௔௕௦ ൌ  ܲ௠௔௡௢ ൅ ܲ௔௧௠ ൌ ͵ͷǤͻͲ͸ͳ‫ ܽ ܭ‬൅ ͻͺǤ͵͸‫ ܽ ܭ‬ൌ ͳ͵ͶǤʹ͸͸‫ܽ ܭ‬   c   $     ! % * ! !       7         " *   ( !              3      $  ' $     (

c c-.c

)$  ሺߛ ൌ ͶͻͲ‫ܾܮ‬Ȁ ݁ ଷ ሻ  ! : '* ! $    "  3   %     ,    !/     .) 2    %  ሺ ݁ ଷ ሻ$  ! ሺ‫ ݏ‬ൌ ͳͳǤ͵ሻ 2! "  !

   c! ! !!/"$   ! %$ 3    % $ $    = c c     c %     cM.)4- -, c c c !" ! "%*"  % !  !    ! -   ! " / :c ! "  ! c      !   $   3  %  ) %          ߛ ൌ ͶͻͲ‫ݔ‬ͶǤͶͺ

ܰ ݂‫ݐ‬ ‫ͳݔ‬ ൌ ͹ͻ͸ͻ͸ܰȀ݉ ݈ܾ ͲǤ͵ͲͶͺ݉ 

 2    ! $    

A



   

6 

C

— "  3% ‫ܨ‬ൌߤ

‫ ܨ‬ൌ ͺʹ‫ିͲͳݔ‬ଷ ൬

ܷ  

ͲǤͷ ൰ ͳ‫Ͳݔ‬ǤͶ ൌ ͺǤʹܰ ͲǤͲͲʹ

.'    "  3*!7 !  !  Ÿ ൌ ߛܸ௣ 

Ÿ ൌ ͹͸ͻ͸ͻ‫Ͳݔͳݔ‬ǤͶ‫Ͳݔ‬Ǥͳͷ ൌ Ͷ͸ͳͺǤͳͶܰ 

‫ ߤܨ‬൅ Ÿܿ‫ݏ݋‬ሺ͸Ͳሻ െ ܶ ൌ Ͳ ‫ ߤܨ‬൅ Ÿܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܶ

ͺǤʹ ൅ Ͷ͸ͳͺǤͳͶܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܶ      #  %    !  

Ÿ െ ܶ ൌ Ͳ ՜ Ÿ ൌ ܶ ܸ௚ ͳͳ͵ͲͲ ൌ ܶ

.  -! !   % 

ͶǤͶͲ ൅ ͵Ͳ͹ͺǤ͹͸ܿ‫ݏ݋‬ሺ͸Ͳሻ ൌ ܸ௚ ͳͳ͵ͲͲ ܸ௚ ൌ ͲǤʹͲͷͳ݉ଷ 4 :" 

  c $ "    !   "  3"  !$ K! $  ! 7 %    *$      $ ! (  3'! " "    !"  (  ! (-   c

c c c

cc-.c 2  ! 01  # *  *!  J!     " ) 0 1  4 .   !  5—*!   "#    

 c c          !    #  *           !   J $     /$  c    c "    (   !     c %  !   ! !    c   = c    ,    ,    , *  %    c   c!   %7  #   !     # *  !   $    

ͲǤ͹ߛ௔௚௨௔ ൅ ͲǤ͵ߛ௛௚ െ ͲǤ͹ߛ௔௚௨௔ െ ͲǤͺ ‫ߛ כ ܵ כ‬௔௚௨௔ ൌ ܲ௔௜௥௘ 

ܲ௔௜௥௘ ൌ ͲǤ͵ ‫͵ͳ כ‬Ǥͷ͸ ‫ͻ כ‬Ǥ͹ͺͻ െ ͲǤͺ ‫Ͳ כ‬Ǥ͹ ‫ͻ כ‬Ǥ͹ͺͻ ൌ ͵ͶǤ͵͵ͻͺ‫ܽ ܭ‬ 

ܲ௔௧௠ ൌ ߩ ‫݄ כ ݃ כ‬

ܲ௔௧௠ ൌ ͳ͵ͷͷͲ ‫ͻ כ‬Ǥͺͳ ‫ כ‬͹ͷͲ ‫ିͲͳ כ‬ଷ ൌ ͻͻǤ͸ͻͶ͸‫ܽ ܭ‬

ܲ௔௕௦ ൌ  ܲ௠௔௡௢ ൅ ܲ௔௧௠ ൌ ͵͵Ǥͷͷ͸͹‫ ܽ ܭ‬൅ ͻͻǤ͸ͻ‫ ܽ ܭ‬ൌ ͳ͵ͶǤͲ͵͵‫ܽ ܭ‬   

.' !   !  !  J 

ͲǤ͹ߛ௔௚௨௔ ൅ ͲǤ͵ߛ௛௚ െ ͲǤ͹ߛ௔௚௨௔ െ ͲǤͷ ‫ߛ כ ܵ כ‬௔௚௨௔ ൌ ܲ௠ 

ܲ௠ ൌ ͲǤ͵ ‫͵ͳ כ‬Ǥͷ͸ ‫ͻ כ‬Ǥ͹ͺͻ െ ͲǤͷ ‫Ͳ כ‬Ǥ͹ ‫ͻ כ‬Ǥ͹ͺͻ ൌ ͵͸Ǥ͵ͻ‫ܽ ܭ‬

ܲ௔௕௦ ൌ  ܲ௠௔௡௢ ൅ ܲ௔௧௠ ൌ ͵͸Ǥ͵ͻ‫ ܽ ܭ‬൅ ͻͻǤ͸ͻ‫ ܽ ܭ‬ൌ ͳ͵͸ǤͲͺͷͷ‫ܽ ܭ‬ c  $  ! % *!!   7    " *(!        3   $ '$    ( c

c c

c

c c c c c c c c c  cc= ccc c

c

c c Í !        * '  ! " :      !  N— (3  /' 3 $ % (   $ 1 "  3   ! " !  "              c c c   c   c ! !  ! !    "  3$ 7 $ $     ! " c   c (c c  ! "!  / !!c (c )     !    c (c )  ! 7' 3   7   !!   /c c   c O  "  -    !   * !        "    ! "  /$ )  c  ‫ ܨ‬ൌ ߛ݄஼  "  3!  !   !    ‫ ܨ‬ൌ ͻǤ͹ͺͻ ൬ͶǤͷ ൅ H! "  

O  "  3   ͻǤ͹ͺͻ ቀͶǤͷ ൅

ሺ͵ െ ݄ሻ ൰ ሺ͵ െ ݄ሻሺͳǤͺሻ ʹ

݄ ‫ ܨ‬ൌ ͻǤ͹ͺͻ ൬ͶǤͷ ൅ ͵ െ ൰ ሺͳǤͺ݄ሻ ʹ ሺଷି௛ሻ ଶ

ቁ ሺ͵ െ ݄ሻሺͳǤͺሻ4ͻǤ͹ͺͻ ቀͶǤͷ ൅ ͵ െ ቁ ሺͳǤͺ݄ሻ ௛ ଶ

G%    (    4   c / ! $ "  3 !"  * !     (   " $      !     !        !   *     "  3   ! " c c

cc 2    *   ! "  37 !    !  :  '$   "  !     4:  "  36$  ! !  @!    !  )   A4P—

   c ! !  ! !    "  3$ 7 $ $     ! "    c c  !    " c c  !       c c   c O  "  -    !   * !        "    ! "  /$ )   c 6  3 3 

6  39 

‫ܨ‬ு ൌ ‫ ܨ‬ൌ ߛ݄஼ 

͸ ‫ܨ‬ு ൌ ͻǤ͹͹͹‫ݔ‬͸‫ݔ‬Ͷ‫ ݔ‬ൌ ͹Ͳ͵ǤͻͶͶ‫ܰܭ‬ ʹ ‫ܨ‬௩ ൌ ߛܸா௡௖௘௥௥௔ௗ௢ 

ߨ͸ଶ ‫ݔ‬Ͷቇ ൌ ͳͳͲͷǤ͹ͷʹ͸‫ܰܭ‬ ‫ܨ‬௩ ൌ ͻǤ͹͹͹ ቆ Ͷ       "  3' 3  ܻ௏ ൌ ܻ஼௏ ൅

‫ܫ‬௏  ܻ஼௏ ௏

ͳ ‫ݔ‬Ͷ‫ݔ‬͸ଶ ͳʹ ܻ௏ ൌ ͵ ൅ ൌ Ͷ݉ ͵ሺ͸‫ݔ‬Ͷሻ 

     "  39 







      ˜  ˜ ½` ˜

    "  3 !    !       "  3'  (  !   7     7  Q ò௖ ൌ Ͳ

Ÿ‫ ݔ‬െ ‫ܨ‬ሺ͸ሻ ൌ Ͳ

ߨ͸ଶ ቆ ‫ݔ‬Ͷቇ ሺʹǤͶሻሺͻǤͺͳሻሺʹǤͷͶሻ ൌ ‫ܨ‬ሺ͸ሻ Ͷ

ߨ͸ଶ ‫ݔ‬Ͷ൰ ሺʹǤͶሻሺͻǤͺͳሻሺʹǤͷͶሻ Ͷ ‫ ܨ‬ൌ ൌ ͳͳʹ͹Ǥʹ͵͸͸‫݉ܰܭ‬ ሺ͸ሻ ൬

  c)! "  3$   *$  !   7     !  "    "  3 !    !     * !   (!  /$ %     ! "  3'  (  c

c

c c-.c Í  !             *    '   ! "   :         !  N— (3  /' 3 $ % (   $ 1 "  3             c c c   c   c ! !  ! !    "  3$ 7 $ $     ! " c c   c !(c c  ! "!  / !!c "(c )     !    c #(c )  ! 7' 3   7   !!   /c c   c O  "  -    !   * !        "    ! "  /$ )  c   ‫ ܨ‬ൌ ߛ݄஼  "  3!  !   !    ‫ ܨ‬ൌ ͻǤ͹ͺͻ ൬Ͷ ൅ H! "  

O  "  3   ͻǤ͹ͺͻ ቆͶ ൅

ሺ͵ െ ݄ሻ ൰ ሺ͵ െ ݄ሻሺʹሻ ʹ

݄ ‫ ܨ‬ൌ ͻǤ͹ͺͻ ൬Ͷ ൅ ͵ െ ൰ ሺʹ݄ሻ ʹ ሺ͵ െ ݄ሻ ݄ ቇ ሺ͵ െ ݄ሻሺʹሻ ൌ ͻǤ͹ͺͻ ൬Ͷ ൅ ͵ െ ൰ ʹ݄ ʹ ʹ

G%    (    4   c / ! $ "  3 !"  * !     (   " $      !     !        !   *     "  3   ! " c

cc-.c 2    *   ! "  37 !    !    '$   "  !     4  "  36$  ! !  @!    !  )   A4P—

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6  39 

‫ܨ‬ு ൌ ‫ ܨ‬ൌ ߛ݄஼ 

͸ ‫ܨ‬ு ൌ ͻǤ͹ͺͻ‫ݔ‬͸‫ ݔ͵ݔ‬ൌ ͷʹͺǤ͸Ͳ͸‫ܰܭ‬ ʹ ‫ܨ‬௩ ൌ ߛܸா௡௖௘௥௥௔ௗ௢ 

ߨ͸ଶ ‫͵ݔ‬ቇ ൌ ͺ͵ͲǤ͵͵‫ܰܭ‬ ‫ܨ‬௩ ൌ ͻǤ͹ͺͻ ቆ Ͷ       "  3' 3  ܻ௏ ൌ ܻ஼௏ ൅

‫ܫ‬௏  ܻ஼௏ ௏

ͳ ‫ݔ͵ݔ‬͸ଶ ͳʹ ܻ௏ ൌ ͵ ൅ ൌ Ͷ݉ ͵ሺ͸‫͵ݔ‬ሻ 

     "  39 







      ˜  ˜ ½` ˜

    "  3 !    !       "  3'  (  !   7     7  Q ò௖ ൌ Ͳ

Ÿ‫ ݔ‬െ ‫ܨ‬ሺ͸ሻ ൌ Ͳ

ߨ͸ଶ ቆ ‫͵ݔ‬ቇ ሺʹǤ͵ሻሺͻǤͺͳሻሺʹǤͷͶሻ ൌ ‫ܨ‬ሺ͸ሻ Ͷ

ߨ͸ଶ ‫ݔ‬Ͷ൰ ሺʹǤͶሻሺͻǤͺͳሻሺʹǤͷͶሻ Ͷ ‫ ܨ‬ൌ ൌ ͺͳͲǤʹͲͳ‫݉ܰܭ‬ ሺ͸ሻ ൬

  c)! "  3$   *$  !   7     !  "    "  3 !    !     * !   (!  /$ %     ! "  3'  (   c

c

c c c c c c  cc= cc c c c c c c c c c c c

c c Í$     !*!! "   '/$ $     !   !     !      !     ) ! !/"  $    ,!2  1! "$ *1! "  3% '7+  $ N— ( ( %! "$ 2   !!    ! " /$   7$  ( !  !$ !  $   /$   "    c  !   $   $      "      /$   "  !    " !   ! %"  3"  '    "  37
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