Fluides visqueux Notes de cours - Alain Le Rille

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d2S S M S
d2S−−→ d2F M −−→ d2M0
−−→
d2F d2S−−→ d2M0
d2S
−−→
d2F
d2S~τ
M d2S
d2S
−−→
d2F=~τ.d2S
~τ −−→ d2S−−→
d2S
−−→
d2F=−−→ d2F⊥+−−→ d2F//
P
−−→
d2F⊥=−P.−−→ d2S
−−→
d2S
•1P a = 1N.m−2
•1bar = 105P a
•1atm = 1,013.105P a
•760mmHg = 760torr = 1atm = 1,013.105P a
~v =vx(y)y < y0
y > y0y0
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y < y0S
y0y > y0
Fx=−η.S ∂vx
∂y
η
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η
1P l = 1P a.s
ν=η
µm2.s−1
ν
ηPl 18 ×10−61,0×10−30,870 103
νm2·s−115 ×10−61,0×10−6635 ×10−61
η ν 20◦C P = 1atm
10◦C20◦C30◦C40◦C50◦C60◦C70◦C
2420 986 451 231 125 74 43
138 84 52 36 24,5 17 12,4
η mP l
dy Oy S
y0y0+dy
•y0~ F(y0) = −η.S ∂vx(y0)
∂y ~ux
•y0+dy ~ F(y0+dy) = +η.S ∂vx(y0+dy)
∂y ~ux
~
Fcis =η.S. ∂vx(y0+dy)
∂y −∂vx(y0) ∂y .~ux=η.S ∂2vx ∂y2dy~ux=η.S.dy∆vx~ux
⇒
~v =vx~ux
d3τ=S.dy ~
Fcis =η.S.dy∆vx~ux
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xOz
y=ys
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