Лекции по гидрогазодинамике
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Q
E
=
Z
(S)
ρ v E dS.
E = Q
E
/G
E = p/ρ + g z
E =
α v
2
2
+
p
ρ
+ g z.
α
v
v =
1
S
Z
(S)
v dS =
Q
S
.
(Re 6 2300) α = 2
(Re > 4000) α ∼ 1
α
1
v
2
1
2
+
p
1
ρ
+ g z
1
=
α
2
v
2
2
2
+
p
2
ρ
+ g z
2
+ L .
g
α
1
v
2
1
2 g
+
p
1
ρ g
+ z
1
=
α
2
v
2
2
2 g
+
p
2
ρ g
+ z
2
+
L
g
.
H = α
v
2
2 g
H
p
=
p
ρ g
H
z
= z H
0
=
α v
2
2 g
+
p
ρ g
+ z
L L
L =
∆p + ∆p
ρ
,
∆p
∆p
∆p = λ
L
d
ρ v
2
2
;
∆H = λ
L
d
v
2
2 g
.
λ
λ ∼ 10
−2
λ
(Re = v d/ν 6 2300)
λ =
64
Re
.
λ
ε = ∆ /d ∆
Re > 4000
λ = 0.11
68
Re
+
∆
d
!
0.25
.
4000 < Re < 20 d/∆
λ
λ =
0.3164
Re
0.25
.
Re
1/
√
λ = 2 lg (Re
√
λ) − 0.8
Re > 500 d/∆
λ
λ = 0.11
∆
d
!
0.25
.
Re
Re
∆p ∼ v
2
•
•
•
•
d
1
d
2
1 − 1 2 − 2
1−2
∆H
.
=
p
1
ρ g
+
v
2
1
2 g
−
p
2
ρ g
+
v
2
2
2 g
=
p
1
− p
2
ρ g
+
v
2
1
− v
2
2
2 g
.
v
1
, v
2
(p
1
− p
2
) S
2
= ρ Q (v
2
− v
1
),
Q = v S =
p
1
− p
2
Q = v
2
S
2
∆H
. .
=
(v
1
− v
2
)
2
2 g
,
∆H
. .
=
1 −
v
1
v
2
!
2
v
2
1
2 g
= ζ
. .
v
2
1
2 g
,
ζ
.
= (1−v
1
/v
2
)
2
= (1−S
1
/S
2
)
2
∆p = ζ
ρ v
2
2
;
∆H = ζ
v
2
2 g
.
ζ
Re 6 2300 ζ
Re Re > 4000
ζ Re
L > (30 − 40) d
L > L
ζ
Q = const
∆p
Σ
=
n
X
i=1
∆p
(i)
+
m
X
k=1
∆p
(k)
.
∆H
Σ
=
n
X
i=1
∆H
(i)
+
m
X
k=1
∆H
(k)
.
L
∆H = ζ
v
2
2 g
= λ
L
d
v
2
2 g
,
L
d
=
ζ
λ
.
L
L = = L (1+L /L)
L