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pm1
1
pm2 = 2 bar
ρ = 1000 kg/m3
H = 5 m
H
ρ
pm1
pm2
ρm
h
H ρ
1 2
2 ρ H
h = 70 mm ρm = 13600 kg/m3 ρ = 800 kg/m3
3
pm
ρ
h
pm = 25 kPa
H = 2 m
ρ = 1000 kg/m3
ρm =
13600 kg/m3
ρm
h
H
ρ
pm
A
h1
h2
ρ1
ρ2
3 4
A
4
pa = 1 ba r
h1 = 0.5 m
h2 = 3 m
ρ1 = 1000 kg/m3
ρ2 = 900 kg/m3
ρ1 ρ2
pm
h1 = 3 m
h2 = 2 m
ρ1 = 1000 kg/m3
ρ2 = 900 kg/m3
ρ3 pdna = 231.3 kPa
pa = 101.03 kPa ρ1 = 890 kg/m3 ρ2 = 1000 kg/m3
ρ4 = 13600 kg/m3 h1 = 1.5 m
h2 = 2.5 m
h3 = 2.9 m
h4 = 0.4 m
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h1 h2
ρ1
ρ2
pm
ρ1
ρ2
ρ3
ρ4
h1
h2
h3
h4
5 6
A h = 500 mm ρ =
1000 kg/m3
A
h
ρ
ρmD
h
H
ρ
7 8
ρ
h = 50mm D = 2 m H = 3 m ρ = 1000 kg/m3
ρm = 13600 kg/m3
pm ρ 9
AB
a
pm = 3 kPa
H = 2 m a = 0.4 m ρ = 1000 kg/m3
pm
A
BH
a
ρ
0 0
0 0
0 0
0 0
0 00 00 00 00 00 00 00 0
0 0
1 1
1 1
1 1
1 1
1 11 11 11 11 11 11 11 1
1 1
0 0
0 0
0 0
1 1
1 1
1 1
M
O
C
H
a
ρ
9 9 10 10
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a
O
M
ρ = 1000 kg/m3
a = 0.5 m
H = 3 m
pm
A A
D
H
ρ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
pm
α
O
F
a
11 11 12 12.
ρ
A
A
H = 2 m
D = 0.5 m
pm = 2 bar
ρ = 1000 kg/m3
pm
O
F
pm = 2 bar
a = 0.5 m
α = 45◦
ρ 13
∆h
∆h = 200mm
D =
100 mm
∆h
U D
V̇
∆h
D2
13 14
ρ
D2
V̇ = 10 lit/s
∆h = 200 mm
ρ
U
pa = 1 bar
ρ = 1000 kg/m3
H = 2 m
U = 2 m/s
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U
H
ρ
H
U
ρ
15 16
ρ
U
ρ = 1000 kg/m3
H = 3 m
U = 2 m/s
pm
U
ρ
H
17
ρ
U
pm = 2 kPa
ρ = 1000 kg/m3
U = 2 m/s
H = 2 m
H
A
B
λ,L,D
ρ
H
λ,L,D
18 19
A
B
ρ = 1000 kg/m3
D = 90mm
L = 7 k m
H = 98 m
λ = 0.02
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H
19
V̇ =
5 · 10−4 m3
ρ = 1000 kg/m3
L = 3 1 m
D = 20 mm
λ = 0.03
A
B
ζ u = 0.5
ζ k = 0.8
λ = 0.02
H = 10 m
D = 150m
L1 = 150m
L2 = 25 m
L3 = 31 m
ρ = 1000 kg/m3
U
ρ
ρ
A
B
H
L1 L2
L3
D
ζ u
ζ k
ζ k
20
d
pm
V̇ = 12.57 lit/s
ρ = 1000 kg/m3
H 1 = 2 m
H 2 = 4.5 m
L1 = 10 m
L2 = 4 m
D = 80 mm
d = 40 mm
ζ u = 0.5
ζ k = 1
ζ m = 0.2
λ = 0.02
V̇
d
ζ m
pm
λ, L1, D
λ,L2, D
ρ
ζ u
ζ k
H 1
H 2
21
P
U = 2 m/s
H = 5 m
ζ u = 0.5
ζ k = 0.5
λ = 0.02
L = 3 0 m
D = 80mm
η = 0.8
ρ = 1000 kg/m3
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U
ρ
H
ζ uζ k
P
λ,L,D
ζ v ζ v
H
A
B
ζ u
ζ v2
ζ kζ v1
P
λ, d2, l2
λ, d1, l1
22
23
A
B
λ = 0.02 ζ u = 0.5 ζ v1 = 2
ζ k = 0.5
ζ v2 = 3
l1 = 5 0 m
l2 = 2 5 m
d1 = 50mm
d2 = 70mm
V̇ = 4 l/s
H = 4 0 m
ρ = 1000 kg/m
3
η = 0.80
