Лекции по гидрогазодинамике
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C Q
tg(δ) ∼ sin(δ) ∼ δ h
x
h = (a − x) tg(δ) ≈ (a − x) δ.
a
p − p
0
=
6 µ v
0
x (l − x)
(2 a − l) h
2
.
h
2
¯
h
2
x
max
p − p
0
p − p
0
=
1
l
l
Z
0
(p − p
0
) dx =
µ v
0
l
2
¯
h
2
(2 a − l)
.
(r, ϕ, z) z
~v = (0, 0, v
z
)
div ~v =
∂v
z
∂z
= 0,
∇
2
~v =
1
µ
grad p.
v
z
= v
z
(r) r, ϕ
∂p
∂r
=
1
r
·
∂p
∂ϕ
= 0,
∂p
∂z
=
d p
d z
, p = p (z).
z
∇
2
v
z
=
1
µ
d p
d z
= .
r z
∇
2
v
z
=
1
r
d
d r
r
d v
z
d r
!
= = C
1
.
v
z
= C
1
r
2
4
+ C
2
ln (r) + C
3
.
r =
0 C
2
= 0 C
1
C
3
r = R
v
z
|
r=R
= 0, C
3
= −C
1
R
2
4
,
v
z
= −
C
1
4
(R
2
− r
2
).
C
1
1
µ
d p
d z
= const = C
1
, C
1
= −
1
µ
∆ p
L
,
∆ p = p
1
−p
2
L =
z
2
− z
1
R
v
z
=
∆ p
4 µ L
(R
2
− r
2
).
v
max
=
∆ p
4 µ L
R
2
.
¯v = Q/S
¯v =
1
S
Z
(S)
v
z
d S =
∆ p
8 µ · L
R
2
=
v
max
2
.
∆ p
L
∆p =
32 µ L ¯v
d
2
.
∆p = λ
L
d
ρ ¯v
2
2
,
¯v
λ =
64
Re
, Re =
¯v d
ν
6 2300.
λ =
A
Re
,
A
A
52
53
57
3.5 × 1) 71
96
Re
Re =
¯v d
ν
, d =
4 S
,
S
G = ρ ¯v S, /c
Q = ¯v S,
3
/c
∆p =
128 ν L G
π d
4
=
128 µ L Q
π d
4
.
~v
~
¯v = ¯v
x
~
i+ ¯v
y
~
j + ¯v
z
~
k
~v
0
= v
0
x
~
i + v
0
y
~
j + v
0
z
~
k
v
x
= ¯v
x
+ v
0
x
, v
y
= ¯v
y
+ v
0
y
, v
z
= ¯v
z
+ v
0
z
.
τ
~
Q =
1
τ
τ
Z
0
ρ ~v (~v ~n) dt.
k
i
q
i
= ρ v
i
v
k
, i, k = 1, 2, 3
v
i
, v
k
q
i
= ρ ( ¯v
i
+ v
0
i
) ( ¯v
k
+ v
0
k
) = ρ ¯v
i
¯v
k
+ ρ v
0
i
v
0
k
v
0
i
= 0, v
0
k
= 0
¯v
i
, ¯v
k
x, i = 1
y, k = 2
q
1
= q
x
= ρ ¯v
x
¯v
y
+ ρ v
0
x
v
0
y
.
x
σ
yx
= −ρ v
0
x
v
0
y
.
v
0
x
∼ v
0
y
∼ v
0
z
.
∂¯v
i
/∂x
k
l