Science of Water : Concepts and Applications

Water Hydraulics 79
and important concepts, we are ready to explain open-channel fl ow in a manner whereby it will be
easily understood.
We stated that when water fl ows in a pipe or channel with a free surface exposed to the atmosphere,
it is called open-channel fl ow. We also know that gravity provides the motive force, the
constant push, while friction resists the motion and causes energy expenditure. River and stream
fl ow is open-channel fl ow. Flow in sanitary sewers and storm water drains is open-channel fl ow,
except in force mains where the water is pumped under pressure.
The key to solving storm water and sanitary sewer routine problems is a condition known as
steady uniform fl ow; that is, we assume steady uniform fl ow. Steady fl ow, of course, means that the
discharge is constant with time. Uniform fl ow means that the slope of the water surface and the
cross-sectional fl ow area are also constant. It is common practice to call a length of channel, pipeline,
or stream that has a relatively constant slope and cross section a reach (Nathanson, 1997).
The slope of the water surface, under steady uniform fl ow conditions, is the same as the slope
of the channel bottom. The HGL lies along the water surface and, as in pressure fl ow in pipes, the
HGL slopes downward in the direction of fl ow. Energy loss is evident as the water surface elevation
drops. Figure 3.20 illustrates a typical profi le view of uniform steady fl ow. The slope of the water
surface represents the rate of energy loss.
√ Note: Rate of energy loss (see Figure 3.21) may be expressed as the ratio of the drop in elevation
of the surface in the reach to the length of the reach.
Figure 3.22 shows typical cross sections of open-channel fl ow. In Figure 3.22a, the pipe is
only partially fi lled with water and there is a free surface of atmospheric pressure. This is still
Channel bottom
Water surface = HGL
L
Q
FIGURE 3.21 Steady uniform open-channel fl ow—where the slope of the water surface (or HGL) is equal
to the slope of the channel bottom.
Air
Ground surface
Pipe crown
Buried pipe
partial flow
(a)
Pipe invert
Stream
(b)
h L
Slope = h L /L
FIGURE 3.22 Open-channel fl ow in an underground pipe (a) or a surface stream (b). (Adapted from
Nathanson, J.A., Basic Environmental Technology: Water Supply, Waste Management, and Pollution Control,
2nd ed., Prentice-Hall, Upper Saddle River, NJ, 1997.)