103104105106107108
10−2
10−1
8
9
1.2
1.4
1.6
1.8
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8
1e−005
2e−005
5e−005
0.0001
0.0002
0.0004
0.0006
0.0008
0.001
0.0015
0.002
0.003
0.004
0.006
0.008
0.01
0.0125
0.015
0.0175
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.06
0.07
Laminar
flow Critical
zone Transition zone Complete turbulence, rough pipes, R > 3500/r, 1/√f = 1.14 − 2 log r
→ →← ←
Darcy−Weisbach friction factor f Í ÄÄÄÄ
2hDg
LV 2
Moody Diagram
r = 5e−006
r = 1e−006
Smooth pipes, r = 0
1/√f = 2 log(R √f ) − 0.8
Material
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
Riveted steel
Concrete
Wood stave
Cast iron
Galvanized iron
Asphalted cast iron
Commercial steel
Drawn tubing
Reynolds number R Í ÄÄ (V in m/s, D in m, ν in m 2/s)
VD
ν
Relative roughness r Í Ä (ε in mm, D in mm)
ε
D
Hagen−Poisseuille equation
R ≤ 2300, f = 64/R
Colebrook equation, R ≥ 2300
1/√f = −2 log(r /3.7 + 2.51/(R √f ))
Acceleration at sea level
latitude 45°, g = 9.80665 m/s2
VD for water at 20°C (V in m/s, D in cm)
0.06
| | 0.1
|0.2
|0.4
|0.6
|0.8
|1
|2
|4
|6
|8
|10
|20
|40
|60
| | 100
|200
|400
|600
| | 1000
|2000
|4000
|6000
| | 10000
|
____________________________________________________________________________________________________________________________________________________________________________________________________
VD for atmospheric air at 20°C
1
|2
|4
|6
|8
|10
|20
|40
|60
| | 100
|200
|400
|600
| | 1000
|2000
|4000
|6000
| | 10000
|20000
|40000
|60000
| | 100000
|
ε (mm)
ÄÄÄÄÄÄÄÄÄ
0.9−9
0.3−3
0.18−0.9
0.25
0.15
0.12
0.046
0.0015
Fluid at 20°C
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
Water
Air (101.325 kPa)
ν (m2/s)
ÄÄÄÄÄÄÄÄÄ
1.003e−006
1.511e−005