Fluides visqueux Les points du cours à connaître

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−→
dF =η∂vx
∂y dS~ux
−→
dF =η∆~vdτ
y < y0S y0
y > y0Fx=−η.S ∂vx
∂y σ
z=z0σ=ηdv(z)
dz z=z0
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µ P µ =f(P)
µ=µ0=cste χ =1
µ
∂µ
∂P
~v =~ 0
Re =µ.V.L
η=V.L νRe 1
Re 1
Re < 2000
~
Ftrainee =Cx
µ.v2
∞.S
2~ux
Re < 1Cx=24
Re Re ∈103; 105Cx ≈cst Re = 5.105
Cx
µ
η α δ
~v =µ.g. sin α
2.η (2.δ −z).z.~ux
~uz
σ
σ=µ.g. sin α.δ
y= 0 y= ∆y
~
F0=F0.~ux~ V=V.~ux~
F0
~
F
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~
V=V.~ux
Ox y ~v =vx(y).~ux
y V
∂vx
∂y F0
V V
∆y
y < y0S y0
y > y0
Fx=−η.S V
∆y
Oz
R
v(r) = −R2
4η
dp
dz1−r2 R2
σ(r) = r
2
dp
dz
R1R2
(Oz) Ω1Ω2
~v(~r, t) = A.r +B
r.~uθ
A B R1
R2
Ω1= Ω2= Ω
A=Ω2.R2
2−Ω1.R2 1
R2
2−R2 1
B=(Ω1−Ω2).R2
2.R2 1
R2
2−R2 1
y= 0 y→+∞
~v(~r, t) = A.e−k.y .cos (ω.t −k.y).~ux
~v(y= 0) = A. cos (ω.t).~ux~v(y→+∞) = ~ 0
` N
a ` a `
∆p
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