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Derive the Navier Stokes' Equation.

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Title: Derive the Navier Stokes' Equation.


1
Derive the Navier Stokes' Equation.
2
1. ????? ??? ??? ??.
                                                                                                                                                      
  • ?? ???? ??? ???? ??? ?
  • ?.

  • (1)
  • ? ???? ??? ???? ??? ??
  • ?? ??? ?? ? ? ??.

  • (2)

3
  • ? ???? ?? ???? ?? ?(1)?
  • ?? ??? ?? ?? ???? ??? ?
  • ?? ?? ????.

  • (3)

4
2. ???? ?.
  • ????? ???? ?? ?? ?????
  • ????? ????, ??? ??? ??
  • ? ?? ?? ??? ??? ?? ? ? ?
  • ?. ?? X???? ???? ??? ??
  • ??? ??? ?? ? ? ??.

  • (4)

5
  • ? (3)? ??? ??? ?? ?(4)? ??
  • ??( )? ??? ??? ???, ?
  • ?? ???? Y,??? Z??? ????
  • ??? ?? ??? ? ??.
  •  

6
  • ? ??? ???? ?(2)?(3)? ? ???
  • ? ? ?????? ????? ??? ??.

7

 
8
  • ??? ?? ?????? ???? ??
  • ??.
  • 4. ?? ???? ??? ?? ??.

                                                                                                                   
9
5. ??? ??? Navier-Stokes ???
  • ????? ??? ???? ??? ??.

  • (8)

10
  • ?(8)? ??? ?(3)? ???? ????
  • ???? ?? ??? ??.

  • (9)
  • ??? D/Dt? ???? ????.

                                                                                          
11
  • ?(9)? ??-??? ??? ???? ?? ??? ??? ? ???,
    Stokes? ???????? ??? ?? ??? ? ??.

12
  • ??? ??? ?? Navier-stokes???
  • ??? ???. ?? ? ?? ????? ?
  • ? ??.
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