Environmental Engineering Reference
In-Depth Information
2
lv
dg
hf
f
=
(2.20)
2
In terms of the flow rate
q
, the equation becomes:
2
f
=
8
flq
gd
h
(2.21)
25
π
where:
h
f
=
head loss (ft).
f
= coefficient of friction.
l
= length of pipe (ft).
v
= mean velocity (ft/s).
d
= diameter of pipe (ft).
g
= acceleration due to gravity (32.2 ft/s
2
).
q
= flow rate (ft
3
/s).
The Darcy-Weisbach formula was meant to apply to the flow of any
fluid and into this friction factor was incorporated the degree of rough-
ness and an element called
reynold's number
, which was based on the
viscosity of the fluid and the degree of turbulence of flow. The Darcy-
Weisbach formula is used primarily for determining head loss calcula-
tions in pipes. For open channels, the
manning
equation was developed
during the latter part of the 19th century. Later, this equation was used
for both open channels and closed conduits.
In the early 1900s, a more practical equation, the
hazen-Williams
equation, was developed for use in making calculations related to water
pipes and wastewater force mains:
q
= 0.435 ×
Cd
2.63
×
S
0.54
(2.22)
where:
q
= flow rate (ft
3
/s).
C
= coefficient of roughness (
C
decreases with roughness).
d
= hydraulic radius
r
(ft).
S
= slope of energy grade line (ft/ft).
2.10.3.2.1 C factor
The
C factor
, as used in the Hazen-Williams formula, designates
the coefficient of roughness.
C
does not vary appreciably with velocity,
and by comparing pipe types and ages it includes only the concept of
roughness, ignoring fluid viscosity and Reynold's num-
ber. Based on experience (experimentation), accepted
tables of
C
factors have been established for pipe (see
Key Point:
A high
C
factor
means a smooth pipe; a low
C
factor means a rough pipe.
