Moody Diagram
Moody Diagram
Moody Diagram
Chapter 8
8-1
Some Concepts and Definitions
Laminar flow Multiple pipe systems
Transitional flow Noncircular conduits
Turbulent flow Major losses
Reynold’s number Friction factor
Entrance region Relative roughness
Poiseuille’s law Minor losses
Moody chart Loss coefficient
Colebrook formula
8-2
8.1 - Laminar vs. Turbulent flow
e
0.06 Re for laminar flow
D
8-5
8.2 - Laminar flow
Laminar flow has a parabolic velocity profile, so that the
velocity at any distance from the centerline,
pD
2 2r
2
2r 2
u (r ) 1 Vc 1
16 D D
2r 2
where centerline velocity, Vc 1
D
8-6
8.2 - Laminar flow
By definition, the average velocity is the flowrate
divided by the cross-sectional area:
R Vc Vc pD
2 2
V
2R 2
2 32
and
D p 4
Q
128
8-7
8.2 - Laminar flow
Poiseuille’s law is valid for laminar flow only!
R Vc Vc pD
2 2
V
2R 2
2 32
and
D p 4
Q
128
8-8
8.2 - Laminar flow in pipes
Velocity and Volumetric flow for laminar flow:
V
p sin D 2
and Q
D 4 p sin
32 128
Darcy-Weisbach equation:
2
V
hL f
D 2
8-11
8.4 - Turbulent flow in pipes
Figure 8.20 - Moody diagram
8-12
8.4 - Turbulent flow in pipes
Table 8.1 – Equivalent roughness table
Table 8.1
Equivalent Roughness () for New Pipes
Pipe Feet Millimeters
Riveted Steel 0.003-0.03 0.9-9.0
Concrete 0.001-0.01 0.3-3.0
Wood stave 0.006-0.003 0.18-0.9
Cast iron 0.00085 0.26
Galvanized iron 0.0005 0.15
Commercial steel
or wrought iron 0.00015 0.045
Drawn tubing 0.000005 0.0015 8-13
Plastic, glass 0.0 (smooth) 0.0 (smooth)
8.4 – Dimensional analysis of pipe flow
The Colebrook equation is
valid for the entire 1 D 2.51
2.0 log
nonlaminar range of f 3.7 Re f
the Moody chart:
V2
hL K L
2g
8-15
Quiz #13
8-16
8.5.2 – Multiple pipe systems
8-17
8.6 – Pipe flowrate measurement
8-18