User Guide

40 l uponorengineering.com
0.001
0.01
0.2
1E+03 1E+04 1E+05 1E+06 1E+07 1E+08
Friction factor — f
Reynolds number — Re
Moody Diagram for ASTM PEX by pipe size — Manadilli Approximation
¼"
5
⁄16"
⅜"
½"
⅝"
¾"
1"
1¼"
1½"
2"
2½"
Figure 4-6: Moody diagram for ASTM PEX by pipe size
Friction loss with
Uponor PEX piping
There are two commonly
accepted methods to calculate
head loss or friction loss in
piping systems. The rst
method, which is preferred
and will be discussed in this
manual, is the Darcy-Weisbach
methodology. The second
method is the Hazen-Williams
methodology.
Darcy-Weisbach
method
The Darcy-Weisbach equation
is a phenomenological
equation, which is directly
related to empirical test data.
This method relates friction in
piping to the roughness of the
pipe, uid velocity, uid density
(water temperature) and uid
viscosity without leveraging
correction factors. This is
the same for systems using
different concentrations of
uids (e.g., propylene glycol).
The following shows a
Darcy-Weisbach equation
h
ƒ
= ƒ
l V
2
• — • —
D 2g
Where,
h
ƒ
= head loss due to
friction (ft)
ƒ = diminesionless friction
factor
l = length of pipe (ft)
D = internal pipe diameter (ft)
V = average velocity (ft/sec)
g = acceleration due to
gravity
All the parameters in the
equation are functions of
system design and layout
except for the dimensionless
friction factor, ƒ. The friction
factor ƒ is derived using the
Colebrook formula which
represents ƒ implicitly.
1
= -2. log
[
E
/D 2.51
]
—– —–– + ——–
√
− −−−−−−−−−−−−−
ƒ
3.7 Re
√
− −−−−−−−−−−−−−
ƒ
Where,
ƒ = diminesionless friction
factor
D = internal pipe diameter (ft)
E = internal roughness (ft)
The roughness of Uponor
PEX-a pipe is 1.58 × 10-6 ft.
Re = Reynolds number
Where,
D = internal pipe diameter (ft)
p = uid density
V = average velocity (ft/sec)
μ = dynamic viscosity
Since the Colebrook formula is an implicit formula, many approximations have been derived to explicitly represent the friction factor.
Using the Manadilli approximation yields a very small error with respect to the Colebrook equation. In fact, the maximum error is up
to 2.06 percent. The Manadilli approximation shown below is used for all Uponor pipe head loss calculations.
ƒ
=
[
1
]
2
-2 • log
(
E
+
95
–
96.82
)
3.7•D Re
0.983
Re
The friction factor can also be found by using a standard Moody Diagram. The Moody Diagram is a function of the Reynolds number
and the ratio between pipe roughness and internal diameter. Below is a Moody Diagram created for PEX pipe.
(
ft
)
——
sec
2
=
pVD
——
µ
(
lb
)
—–—
ft
3
(
lb • sec
)
ft
2