Environmental Engineering Reference
In-Depth Information
2
h
L
2
h
L
V
1
2
g
V
1
2
g
Energy grade line
Energy grade line
2
V
2
2
g
2
V
2
2
g
Water surface
Hydraulic grade line
y
1
y
1
V
1
Piezometers
V
2
y
2
y
2
V
1
V
2
Channel bottom
z
1
Center line of pipe
z
1
z
2
z
2
Datum
1
Pipe flow
2
1
Open channel flow
2
figure 2.15 Comparison of pipe flow and open channel flow. (Adapted
from Metcalf & Eddy,
Wastewater engineering: Collection and Pumping
of Wastewater
, McGraw-Hill, New York, 1981, p.11).
operations and practice. Although the subject of pipe flow embraces
only those problems in which pipes flow completely full (as in water
lines), we also address pipes that flow partially full (wastewater lines,
normally treated as open channels) in this section. Also discussed is
the solution of practical pipe flow problems resulting from application
of the energy principle, the equation of continuity, and the principle and
equation of water resistance. Resistance to flow in pipes is not only the
result of long reaches of pipe but also affected by pipe fittings, such as
bends and valves, which dissipate energy by producing relatively large-
scale turbulence.
2.10.2 Pipe and open flow basics
To gain an understanding of what friction head loss is all about, it
is necessary to review a few terms presented earlier in the text and to
introduce some new terms pertinent to the subject.
*
energy grade line
—The total energy of flow in any section with refer-
ence to some datum (i.e., a reference line, surface, or point) is the
sum of the elevation head (
z
), the pressure head (
y
), and the velocity
head (
v
2
/2
g
). Figure 2.15 shows the energy grade line, or energy gra-
dient, which represents the energy from section to section. In the
absence of frictional losses, the energy grade line remains horizon-
tal, although the relative distribution of energy may vary among the
elevation, pressure, and velocity heads. In all real systems, how-
ever, losses of energy occur because of resistance to flow, and the
resulting energy grade line is sloped (i.e., the energy grade line is
the slope of the specific energy line).
*
A more complete listing of hydraulic terms can be found in Lindeburg, M.R.,
Civil
engineering reference manual
, 4th ed., Professional Publications, San Carlos, CA,
1986, pp. 5-2-5-3.
