Mécanique des fluides

July 22, 2017 | Author: coursenligne.lille1 | Category: Laminar Flow, Pressure, Fluid Dynamics, Viscosity, Fluid Mechanics
Share Embed Donate


Short Description

Download Mécanique des fluides...

Description

           

        

       

 







           ! "! #"$ " "! " "%  !%   "&!   "'#(   ")(!*! +!  %,-  .-#+ #.-*   &! ! +!) %!)  "  #"/0(  "!!  "*#!  "-!#   "-#$   "-# "1   ' 1!  "   #" (2 





  "(  #"(,-  "1  "%(!  "% # 3-( 4/!(!  " #5-67  #"   " !!  "8( %-' %+896 %"  )" (    ' + "! #"1 "6 "% "6("--  %-' %+'89,/2: "6#  !  "%(  #"%"-;   %-' %+'89,#!#6'?@B9/%- !  &)7@! %5$$"'9+/8&@ +'89%-%=>6'?@  &)7@!  !"#$%&#'#!&"$(!)  (C,A6'DD (E,(='+&)7@!DDD5







     *+,%&-,.,(/#  0 &  !F      5   F   1   (!!        !   (5 0 -      5   F   1        ! !   #5 -   1#   #5 '     !   5 09FF #5-(21##5 0'(2F!!! !5     1+-"(&',#2,(   @F(2F!1( ,1(!      (     5 -  !   !5 @       15        !5  1F!( F5!F!# !!*!, 5   3+#%%(!)   6        !      2F'.!25  6*∆ ∆!! 1∆ ∆2F'!    ∆2  2 ∆2  '=  =   ∆→E  ∆   ∆  



3

 -!1# 5!5  -!,%$,-GHI9.  @!!!,4,#  #IE3            ! "#   ! #$ !% !%%   5+,%%6!-".(7"   @ !   (   .        ρ G1!7(H ρ=

. 



!5 -!!, .#1#F! !5(!!Fρ (F(,  ρ(Τ) ≈

ρο 

 *J  *EEJ  *EJ 

  .

EEE7( D3K7( 3D47(

(2F  '5 ρ ,( '( (,

' ρ (Τ, ' ) ≈ ρ  0 

 %*EJ FI# %*EJ FIEFD# %*EEJ FI#

FD7( FD7( EFD37(

 &!,$ *+:*J 5   *EEJ  EFD3K *EJ  F3D4    (2  !!     :   +   G  !  !+H5   

!

!"#$

%

&' (

ρ

#

# ) # (

* (

+

(

+

=)

%

* !

* ( "#

(

+, $ +

#

%

(

&

*

=

+

=ρ # (

(

= ρ+# = ρ+ - − - (

*

)

'

-

& -

-. -( / - - / - . -, / (. (/ , (

=*ρ+ -

+

- *

-+ - = ρ+ -

-. -

+

,

-

-

#

.

/

-

/ .

0 )

* /

+ ρ+# # ρ+#

/

& 1

# /

/

= ρ+# .

#

1

#

2

2

3

4

3

#

4

(



5 6777

+

=

+ ρ+#

2777 × 27 × 6777 ≈ 672 2 723 27 6

! '

&

/

=

0/





. )

1

8

80

81



.

=*ρ+ -

4

'

1+

="

8

*

-

& "

# /

"

) & * ) /2; & % = 32? × +93 = = ≈=< 1+ +> 27 "3 × > =2

5 +93 : )

# ="

-

#

$ )

*

&

/37 <

- =

-

)

*

-

*

4

ρ - =ρ )

) = 2

*

-

)

1

ρ =

*

-

)# + ≈ 6677

-/ -

* % #4

- / 33)) 3)

)

)

)

2

- / *3))) 5

! #≈ $%&"'()( ( *

" ρο 0

ρ #

0 ρ 0+

( / (

/ ρο0+

ρ0

0

)

?

/ %

ρ > ρο " # " @

%

ρ0+ / . * #(

# =

)4

=

"

+ ρο =

ρο

% ) .

*

)

=

(

* = ρο

"

)4

(

+ ρο

* #

A (

/ %

#

%

=

B

+

/ )ρ * ρο)0+

#

ρ

#(

ρ0

! ! " !

#

$

(

+

"

, -

'

'

/ )

/ ρ0+

$ .

! +

ρο 5 2777 < C * , 5= 0 ρ − ρ0 / ρ 6 ρο 0+ = ρ

ρ , 5 27 0

3

ρ = ρ0

/

(

0 ρ 5 27+6 < C

3

ρ 5 >+7 < C 3

*

= 3))) 8+

7

&

6

E Gi

/ ρ+0+ D

4 4

/ρ 0 + ) A

& E

!

% 0" ρ+ 0 :2) = = ),9:9 = 0 ρ )23

#

/

1 2

/

@

. ρF 5 7 29= < C 3

2

/ 4 )

3

#5 4

*

& ρ/ 0 ρ

>7;

3 4

"# "# "# (

E

A 5 277 )7 2 3* G ρ 5 2 +> < C 3H & 5ρ A 4 5 ρ FA 54 I4 4 5 )ρ J ρF*A 5 )2 +>3 J 7 29=* × 7 2 × > =2 5 2 7> 0 277 277 277 < & *

% !

4

277

%

D

) * 4

(6

/ %

( (

"

3

K

;

< ' #5 4

% !=

%% #$

'!&'

@

(

(

∆ = ∆ =

(

#

&

/

%

#

( $ (

(

(

(

=

(

(

( (

( (

#

7 1 %'

%

%%

%

#

&

(

&

"

5

!

#

6

'

(

$

L '

)

> *

)



&

/ ),

)

+ +#

/ #

=ρ 4

# N N N

+ +#

#=

ρ

patm

++

ρ + M23K77 < C 3 )2 723 276 4 *

2 2 # + ' 3 ρ

/ 2 723 27 6 #= = 7 9K 23K77 × > =2 /9K7

F / /2

# F

) 3

2

= 9K7

5 2777 < C *

"

2 723 27 6 #= ≈ 27 2777 × > =2

.

9

5

!

(

3 + @ .

D * # *

) )

#

/

/

?

=ρ+#

* =

& =

?

#

=

+ρ+#

?

#

&

/

#

ρ+#

#

"

%

5. "6. "O

!J O

#

( / )

& -

%

=

+ρ+#

%

* 4

! "

#

$

$ %

&

$

(

&

'

&&

' *

%

& $

& )& #

& &

+, * !

' $

&

&

& & &

& '

&" (

&

& $

$ &

$

. & &

$

& &"

/$

-

&

$ &

&" &

&

'

&

&

)& )&

&

-

!

. & &

&

'

& ∆ ∆

&

0

∆ ∆ %



&





1

&

&

&

∆ !" # -

& &

#

& $ $

#

$ $*

&

$

&

"

$

$

*

2

! % &

&

$ $

&&

&

* ,

&

)

/

! & &

)

=

) )

=*

& π'

)

= *π

' (

,

=

&

'( %

+ *

)> )

&

(

&

&

&

4& &

& 56 !

$ %

*

$

, '-." !" $"'

!

&

&

&

#

, =

=

& '

&

! &

/$

$

$

'

& &" &

(

& &"

&

$ 3

&

&

&

& $ $

&&

$

!2&

&

$

& $

&

(

*

&

& & $

&

/$

$ $

/

&

0

&

#

7

%

,

&

&

&

)'"





.

+∆

#

)

)'"

∆ -

#

1

∆ & & &

ρ &

* $ %

& ∆ #

ρ∆ 4



5

$

3

4

25

4



=



$

2=

∆ ∆

$

3

=

=



$

$

∆ ∆

0 ρ ∆ 4/ 3 / 2

1

)

$

$

&

4)

ρ4

$

3

3 )$ $ ∆ $ =∆ =

' 8

ρ0/

5ρ0/5) #

8

"

&

, )

#

$

& !

#

$"'

8

)

' +"

3 ) $ 2 = ∆)

&

ρ

%

$ $

3 ) $ 2∆

2 5 ρ 0 4/ $ 3 / 2 4)

ρ



$

& )'"

$

&

1 $



∆ = $ ∆ = $

)

0 ∆. 4/ 3 / 2

)

)

)'"



$

$

* !

ρ∆

2

)'"

)'"

∆.

&



+"

#

:

$

! 9 $

;

*

))&#

! , '-." !" $"'

&&

ρ 0 4/ $ 3 / 2 )

6 &

&

3 )$

",

< &

&= ρ

)

5ρ0/ 5) )

ρ

)

!

5ρ0/ 5)

#

#

ρ

#

5ρ0/ 5)

& & * ρ0/ 5) )

#

-

&

&

ρ0/ 5)

)

&" !

( -

!&

& ρ0/ 5)

#

&

(

/)

/#

/ /

$ ) 3 ) )

) 3 )

ρ 0 4/ 3 /

#

#

)

3 ρ 0 4/ 3 /

#

/#

#

ρ > ?7@7 A )# ≈ ??<

' ! & / > B /# > ) @C??< )) C;D??< ≈ C)# 8) $

&= $ 1

$# /)

! %

* && "

&&

8 & &=

& & $ =0

-

)# ρ 0 4/ 3 / # 2

& &

&

5

(

$

0 0 E

&

$

&& & &

) = ) − ρ 40 + 2 4/ 3 / #

)

6

#

&&

3

& 1

$ $#

≈ 7 0

"

6

B

% 5

$

&&

8&

&"

# $ !

" ρ

4 &

5 ρ0/

& * #

)

)$ =

$

$

=

$

5 ρ0/

$

5)

$

& ) &

" &

.

.

& $

$

1 ρ0/

ρ

5ρ0/

$

$

04/ − / $ 2

$) #

+

$

&"

$

"

/ 3 /$ '

&

'

0%

)

&

≈6

& "

ρ

5)

$

$

6

&

/ , ,$ $

& :

$

!

ρ

-

$

/

> /$ =

5 ρ0/

ρ

5)

" 9

$

&

$

!

$

$ $

5 ρ0/ 5)

$

)

F

3 )

G

$

) 3 )$ F ? <

)

ρ(

$

$

3 )

$

$

3

2

/

$

,#

(

#

& &

$

=

& $

ρ

3 $

D

% &

&

)

3 )

*

$

&

",

&

$

& H %

&

&

$ ∆"> "4 I ": > D & ∆ > C∆

% C = 4

ρ

4

C

4 -

6 4

I

*& :



# -: > ? -4

#

∆"> ?7@7 ×@D× ???D> D <

≈ C 7& 0 .



:

C0 %

$

< 4

1

$

&

&

ρ0/

ρ

5)

$

$

ρ

$

5)

$

$

4

=

ρ

4) − ) $ 2

: %

& ) 8 )$

, $

& :

&

,

)

$ &"

ρ0 ,

E

5 ρ0/

$

5)

$

:

$

(

=

0,

4

<

!# % %

(

&

& $ *&

$

&

$

*

&

% "

&

&

!

( K &

#

9

$

9

* "

5 !

1

&

&

J

5 !

& #

&

@

: $

$ *& "

$

& % "& & <

*

%

& & &

! "&

! ",

, 3

&

$

-

$ & $

'

6

)'"

)'"

)'"

')'"

#"

:

-

&

!

&

9

, -

&

) '

& % #"

5, &

+

&

: &

"

! %

C C

& &

&

&

*

&

" ,

! #

$ !

"

#

&

$ ∆$ ' ∆"

(

) ∆$ (

)

∆" ∆$

'

"



∆" ∆$

η ( [η] =

+

"

%

*

" + ∆" ∆$

"

(



[ " ] × [∆$ ] [ ] [∆" ]

(, ×

-

). = ,

'

,

/

' η

η

% ) (η

% 01 01 5 01

η

!, 23 .

#

η

!, # . 4 . )3 . . )3 6.

)3

η

!, 3.

.

)3

#

)3

! 36 01#

.

η

1

%

7 ) (η

η

% 01 01 5 01

η /

!, # .6 . )3 .4 . )3 .8 . )3

)' )'

9

$

'

7

'

'

7

$ "

%

(

+ρ+∆ * )*

" )" (

)

= ∆

(

& ( ∆

" - "( (

7

( ∆

7

"

ρ∆

(

=

)



(

(

)

7 * - *( =.

)= ∆ (



"

)

(

)+

+∆

+

"

*

,

9 -

(

"

(

"

=

)∆

!

#

' )

(

"

(

(

(



=

1

"



#

$

' &

$ !, 8 . )3 83 . )3

&



(

1 "

&

7 /

'

/

"

,

$

"/ 0

:

/

/

!

(# '

; (

1

(

)

<

)

=

)

=

= π

(

"/

' π

" = −η

/

" =) π

η

"

∆ η

"/ 0 - .

=)

(0

= π



"/

+

0

(

-

π

"

∆ -

":

/

7

'

∆ -

)

;

0

1 7 "

/

"

"/ 0 = ∆

"

,

"

'

7

"/ 0 ) "/ 0 = −

'

/

) # 2η

"'

= "/ = .0 =

∆ 2η

>

∆ η

"

3

'

=

7

> π

! π ∆ 4η

=

2

!

"

"/ 0

7

#

3

7 /



#

=

η

4 η π /

2

(



η

* !

7

$ #

( * " =

" !

/ ∆

=





'

"'

/

"

'

7

"=

???) #

$

/

=

=

π ∆ 4η π

2

4 η"

>5

>.

3

@

- .

B =

4ηA π

('

=

5

4× .

/

& A &



)3

×.

3 .5 × !5. $ ; 5 A

)C

× .

−3 5

≈ , !

.2( 7 D . 25 ≈ 2

7 5

2 7

∆ 7

. /

=

D



( '



7 #

#

A

/ ;

/

$

;

4D

4 ηA

π

/

5

∆ =

4 η A@. E π( 4)5

= ∆

45 ≈ 5. ∆ .

, (

5

=

=

= "= ∆ " = /

!, *

7

=

'

(

0=

∆ # (





,

)

=

4 η

π

2

)∆



)

7

7 5

! = ∆ =6

* 6

5

# ∆ -6

!

!6

/

!

6

'

=

!

4 η

π

,

2

7

/

@

3

>. 3

>.

=

4× . ) 3 × , 3,.5 × !. 3 .

)

#

5

≈ 32 F,

H /$ /$ ∆ C . ∆ > . F, *

3

@

)2

3

≈3

3

2,

@ '

( @

3

H

1

(

) &

7

$

7

( %

=

=∆

≡ ∆ 6

)&

)5

>

< <

#

7

!

6 !%

6% !

7 (

;

= 6

!

2



=

%



=

6

!



6%

6 !% =

!

6!

( +

/ )

/ /

5$

7

* (

! /

73 7 /

∆ 7

/

6! A

; $



=< A .

A =∆

,

.

; 7

.

= ∆

=.<

. <

/

∆ =A

< .

∆ =∆

'

7

$

1

2

/

< =

4 η π( 4)5

. 4D <

/

= 45 <

45 ≈ 5. ∆ .

7

7 7

; ' '

,

7

7

/

*

(

)'

7 / 7

)'

"

"



'

7 $

?

7

$

7 7

6

=

ρ" η

!

η 1 ) )

/

< /

7 "

6(

ρ

/

# $ K 6 L3

,

'

(

6

7

C

7 ' 7

"

6

" * 6 ≈

" ! @# (η= η= 10 , ρ >. 1 10). 10−2 −3

. 10 .

1

!

3

2000 η ! 2ρ

... " =

3

F @

3

"# (

" ! @# (η= η= 2.10 , ρ >. 3 F @ .2 5 . 25 .2 −5

#

3

#

#

. '

7

$

$ ;

$

7

< /

*

!

<

' H ρ η

=

#

/

!

" >3 @ ×. 2 × 3 × 2. = . )3

/

> 2 ) D

/ )

≈ .C

!

/ #

A

D



=



=

4× . ! 2.

)3 )

× 3

≈ .8 , @

#

A >.

/

D <

'

#

≈ 7

=

ρ η A =π

=

η

≈ 3.

<

ρ )2

. −3 × ≈ ×. × 3

@

!

. @

≈ . @ #

/

6

8

+

! / / ! / /

# # 7

H

! ;

7 7

#

A 7 1

7

'

M

/

(

/

'

/

>5 . > 563 .

!5 µ #

)C

2

6 !%

$ < =

,

4 η π

5

N



.

.C

,

@

. 3 F @ .C .C . )3 .C . )2

#

$

!

# •



: 6

(

7

3

#

7

3

) : 6

7 > 2.105,

$

)

6

" > .55 F @ !5

>

)

N 7/

F

" > .55 F @

>3

" > 3C F @

@#

6 : 6 > 5.10 , 7 : 6 > 3.10 .

$) *)"+% , $

" η

7 ' ) ' ) ' ) ' '

$

ρ

/ ρ

(

"

3

Q

$ "

3+

+

"



=. 7

* 3 = ρο +

2 = π &

-ρ + !

ο

( &

#

"

"

-3 )

=9πη

"

3

+ /ρ ο − ρ) > η $ ! > . µ ρο > 7 > 5 @ " =

1 , !η > . 4. .

)2

ρ >. 3 F @

,

3

#

η

(

<

=

ρ

#

)

( *

& F = 3 5.

η

3

F @

)

ρο # η. '

ρ P (

" )

R

=

3

)

Q

ρο =

$

ρ

& F

)

3 +

+

"

"

=9πη

"

=.

+

"

=3

7$

;

"

=

7

> η

/ρ − ρ 0

3

ο

ρ

=

ρο

' 9πη

)

ρ ρ

ο

"

T

ω

6

(S N < / T

7

!ρ = .32 F @ 3# ( > . .3 . ( 2

)

F

! ρο = . F @ 3# / > 2 . )3 µ

(

>

ω > π ≈ .5 @ P ( > ω < > .5

T Q =

. .3 . − × . C C × 3 .5 × C8 . ) 3 × 2 .

'

)8

× .)

×

. ≈ 5 5. . 32

.C $

@

.

2≈. )6

C

@ ≈.

@ "

2

!

"

"

" "

#

" $% ! #" " $% & ' ! !

( " ! " #

"

"

%$#

"

$$

) "

" *

"

"" )

" "

" "

"

" " ,

"

"

+

-

" "

" "

" "

. -

0γ "

" "

" "

"

= γ

"

/

" $ '

! " !

#. !

"

# ""

-

%

∆%

-





"

γ= γ= ! γ

& γ ∆% 1 γ ∆ "

1∆



"

#∆

1γ ∆ "

,

"

" !

& ∆% " % "

"

2

∆4 ∆)

3

"

" /

5

γ

-

"

6

7 4

/ 4 @A 4

89 :
View more...

Comments

Copyright ©2017 KUPDF Inc.
SUPPORT KUPDF