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Ejemplos-bmacroscopico Cm (1)
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8/17/2019 Ejemplos-bmacroscopico Cm (1)
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8/17/2019 Ejemplos-bmacroscopico Cm (1)
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B
W
B/2
Ae
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w = 0
Ae ρ(v · n)dA = 0 = −v1A1 + v2A2 + v3A3
. . .
A2 = A3 = A1/2
2v1 = v2 + v3
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n = -i A
1 A
S
n = +j
n = -j
n = +i
p0
gy
x
A2
A3
AVC
L
AVC
I
AVC
S
AVC
R
v1
v2
v3
AI V C
AS V C ALV C A
RV C
AI V C = AS V C A
LV C = A
RV C
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v2 = v3 = v1
0
ddt V (t) ρvdV + Ae(t) ρv(v −0 w ) · ndA =
V (t)
ρgdV 0
+ A(t)
t(n)dA
Ae
ρv(v · n)dA =
Aa
t(n)dA =
Aa
[−n p + τ · n]dA
y
j ·
Ae
ρv(v · n)dA = j ·
Aa
[−n p + τ · n]dA Ae
ρvy(v · n)dA =
Aa
[−ny p + (τ : nj)]dA
ρv22A2 − ρv23A3 = ASV C − p0dA + AI V C p0dA + AS (τ : nj)dA
F y
0 = F y
F y
F y =
AS
(τ : nj)dA
x
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x
i ·
Ae
ρv(v · n)dA = i ·
Aa
[−n p + τ · n]dA Ae
ρvx(v · n)dA =
Aa
[−nx p + (τ : ni)]dA
−ρv21A1 = AL
V C
p0dA − AD
V C −AS
p0dA + AS
[− p + (τ : ni)]dA
−ρv21A1 =
AS
p0dA +
AS
[− p + (τ : ni)]dA = p0AS + F x
F x = −ρv
21A1− p0AS
−F x
F a =
AS
−(i ·n) p0dA =
p0AS
F N x = F x − F a = F x − (− p0AS ) = −ρv21A1
−F N x
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t∗(n) = t(n) + n p0 = −n p + τ · n + n p0
t∗(n) = −( p − p0)n + τ · n
p0
pm = p − p0
t(n)
Aa(t)
t(n)dA =
Aa(t)
t∗(n)dA −
Aa(t)
n p0dA =
=
Aa(t)
t∗(n)dA −
V a(t)
∇ p0dV =
Aa(t)
t∗(n)dA
∇ p0
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v20 = v22
Ae
ρv(v · n)dA =
Aa
t∗(n)dA =
Aa
[−n pM + τ · n]dA
= Aes [−n pM + τ · n]dA + As [−n pM + τ · n]dA
Aes
As
t∗(n) = 0
F
Aes
Aes
x
i ·
Ae
ρv(v · n)dA = F x
ρ(+v0)(−v0)A0 + ρ(+v1 cos θ)(v1)A1 = F x
F x = −ρv20A0(1 − cos θ)
y
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“0”
“1”
n
n
Θ
y
x
F
A0= A
1
θ
j ·
Ae
ρv(v · n)dA = F y
ρ(+v21sin θ)(v21)A1 = F y
F y = ρv20 sin θA0
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D0 D2
A0
A2
t∗(n) = − pM n + τ · n ∼ − pM n
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D0
D2
p0, v
0 p
2, v
2
VC
A0
A1
A2
n = -ez
n = +ez
n = er
n
r
z
D0 D2 A1 A2 − A0
−v0A0 + v2A2 = 0
v0 = v2
D2D0
2
z
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Aes
ρvz(v · n)dA =
Aes
− pM (n · ez)dA +
A1
(− pM n + τ · n) · ezdA +
+
AL
(− pM n + τ · n) · ezdA
−ρv20A0 + ρv22A2 = p0A0 − p2A2 + p1A1 +
+
AL
[− pM (er · ez) + τ : erez] dA
−ρv20A0 + ρv22A2 = p0A0 − p2A2 + p1(A2 − A0) +
+ AL
τ : erezdA =F vz
Aes
A1 AL
Aes A1
AL
A1 = A2 −A0
AL
F vz
p1
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A0
p0 ∼ p1
v22
v20
p0 − p2 = ρv20
D0D2
2 D0D2
2− 1
D0/D2 p0
A2 A0
