Civil Engineering Reference
In-Depth Information
The Darcy-Weisbach formula is:
LV
2
H
ƒ
(26-5)
DW
D
2
g
where:
H
DW
headloss, ft (m)
ƒ
roughness coefficient, which varies with pipe sizes, roughness, velocity, and
kinematic viscosity, dimensionless
D
diameter of pipe, ft (m)
L
length of pipe, ft (m)
V
average pipe velocity, ft / sec (m / s)
g
acceleration of gravity, 32.174 ft / sec
2
The value of ƒ is expressed as a function of the Reynolds Number (Re
VD
/
V
, where
V
is the kinematic viscosity) and can be obtained from the Moody diagram (Fig.
26-2).
3
The Manning formula is:
1.49
V
RS
(26-6)
2/3
1/2
n
1.0
V
RS
(metric)
(26-7)
2/3
1/2
n
where:
V
velocity
n
Manning roughness coefficient, dimensionless
R
hydraulic radius, ft (m)
cross-sectional area of liquid divided by wetted perimeter
S
energy slope, ft / ft (m / m)
Table 26-2 lists typical values of
n
, for closed conduits flowing partly full for various
pipe materials.
The Hazen-Williams formula is the most commonly used formula for water plant
hydraulic calculations. Tabulated values of headloss per 1,000 feet can be found in
Williams and Hazen.
4
The headloss is given for various pipe sizes,
C
HW
values, and
flows, which allows simple calculation of the expected friction losses.
The Darcy-Weisbach equation is sometimes used because the headloss is expressed
in terms of a constant times the velocity head, as are many of the other system losses.
Although the Manning formula is more typically used with open channel flow, it
can be applied to pipes flowing full.
Hydraulic Component Head Losses
In calculating the headloss in a pressure pipe system, the headloss for each component
of the system is determined in terms of the velocity head as shown in Figure 26-3.
The headloss can be defined by the following equation:
