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Fiches mecanique des milieux continues - hydrodynamique

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3 fiches sur l’essentiel du cour d’hydrodynamique de L3 - conservation -fluide -Bernoulli -fonction de courant

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  • February 23, 2022
  • 3
  • 2021/2022
  • Class notes
  • Unknown
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MW-quemmihuxw-hydro-dynamjqueecoulfonction
ement.it
ami naire =
mouv
régulier de courant
et ordonné couches
glissent l'es Vn
3¥ Vy -3¥
,

une sur les autres = =
;
Vr
-1,3f,
-




;


turbulent : déplacement particules Vr = Vxcoso +
Vy sino
Vz la ¥ =
-




irrégulier fluctuation
,
aléatoire
,
n' n' +
2
et x= ruso
y
=




rmio
Description Eulérienne mourir décrit : y =




pour tracer
:
4=4
par champs de vitesse Tifrit)
les lignes : .




Yo =
0 Yo > o t y ) >
Yoco (→ x
)
, ,

Lagrangienne : arc position initiale ouz ouz
T'tri ,
t)




lignes de courant équation de conservation :




d-n' ai:-O al
dj-n-djt-y-ds.gg
'


→ + diolfv ) =
0
j

lignes d' écoulement =
trajectoire
⇐ >
¥ + pdiv J' =
0


et incompressible
particules de fluide fluide compressible
lignes d' emission courbe de l'ens = .

dépend de la nature du phénomène
des particules passant en 1- point et conditions de l' écoulement

écoulement stationnaire : J' ind .
t incompressible : = 0 → div J' 0 =



lignes confondues
écoulement incitation nel : ààtv :-O
Accélération d' une particule
DJ
mouv .
et déformation

à
.EE?E--an+fIE-a?Yoniec#ee
T gradient se

ÀÀ) À
tenseur

È Èt )
de vitesse

121=6 1213¥ +3¥;)
= "+
+
eij
=
mou , =

,
( on troue les coordonnées )
'

de à
à =
IE -
Êt )
wij =

Effi -3¥;)
°Ë=Ô
.




Si écoulement stationnaire :

Vorticité Û Ünv ( citerne rotation
'


: =



Variation densité ou température : des particules sur elles -
même )
J' FT
¥ 3¥ = + J' Tt
,
=
¥ +


force de surface
conservation de la masse
fluide à l' ext du volume .




débit en volume : Q =
SÇJ ? d-s' DË E. d-s' ÈÂ ds ( force
= f.) = .
num


Pression d-Ép PÏDÎ ( isotrope )
Q
Ypj dj
en masse :
=
: = -




.

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