Science of Water : Concepts and Applications

Water Hydraulics 69
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V 1 2 /2g
y 1
z 1
1
Energy grade line
Hydraulic grade line
V 1
Piezometers
Center line of pipe
Datum
Pipe flow
V 2
2
h L
V 2
1 /2g
V 2 2 /2g
y 2
z 2
Open channel flow
V 2 2 /2g
and the velocity head V 2 /2g. Figure 3.15 shows the energy grade line or energy gradient,
which represents the energy from section to section. In the absence of frictional losses, the
energy grade line remains horizontal, although the relative distribution of energy may vary
between the elevation, pressure, and velocity heads. In all real systems, however, losses of
energy occur because of resistance to fl ow, and the resulting energy grade line is sloped
(i.e., the energy grade line is the slope of the specifi c energy line).
Specifi c energy (E)—Sometimes called specifi c head, is the sum of the pressure head
y and the velocity head V 2 /2g. The specifi c energy concept is especially useful in analyzing
fl ow in open channels.
Steady fl ow—Occurs when the discharge or rate of fl ow at any cross section is constant.
Uniform fl ow—Occurs when the depth, cross-sectional area, and other elements of fl ow
are substantially constant from section to section.
Nonuniform fl ow—Occurs when the slope, cross-sectional area, and velocity change from
section to section. The fl ow through a Venturi section used for measuring fl ow is a good
example.
Varied fl ow—Flow in a channel is considered varied if the depth of fl ow changes along the
length of the channel. The fl ow may be gradually varied or rapidly varied (i.e., when the
depth of fl ow changes abruptly), as shown in Figure 3.16.
Slope (gradient)—The head loss per foot of channel.
y 1
z 1
1
Energy grade line
Water surface
Channel bottom
FIGURE 3.15 Comparison of pipe fl ow and open-channel fl ow. (Adapted from Metcalf & Eddy, Wastewater
Engineering: Collection and Pumping of Wastewater, McGraw-Hill, New York, 1981.)
FIGURE 3.16 Varied fl ow.
RVF GVF RVF GVF RVF GVF RVF
Sluice gate
Hydraulic
jump
RVF – Rapidly varied flow
GVF – Gradually varied flow
V 1
Flow over
a weir
V 2
2
h L
y 2
z 2
Hydraulic
drop