Environmental Engineering Reference
In-Depth Information
Free water surface
We tted perimeter
2.0 ft
3.0 ft
figure 2.20 For Example 2.15.
Example 2.15
Problem: A rectangular drainage channel is 3 ft wide and is lined with
concrete, as illustrated in Figure 2.20. The bottom of the channel drops
in elevation at a rate of 0.5 per 100 ft. What is the discharge in the chan-
nel when the depth of water is 2 ft?
Solution: Assume n = 0.013. Referring to Figure 2.20, we see that the
cross-sectional flow area ( a ) = 3 ft × 2 ft = 6 ft 2 , and the wetted perimeter
( P ) = 2 ft + 3 ft + 2 ft = 7 ft. The hydraulic radius ( r ) = a / P = 6 ft 2 /7 ft = 0.86
ft. The slope ( S ) = 0.5/100 = 0.005. Applying Manning's formula, we get:
20
0013
.
q =
× ×
6086 66
..
×
0 005 559
.
.
=
cfs
.
2.12.3 open Channel flow: The bottom line
To this point, we have set the stage for explaining (in the simplest
possible way) what open channel flow is—what it is all about. Now that we
have explained the necessary foundational material and important con-
cepts, we are ready to explain open channel flow in a manner whereby
it will be easily understood. We stated earlier that when water flows in
a pipe or channel with a free surface exposed to the atmosphere it is
referred to as open channel flow, . We also know that gravity provides the
motive force, the constant push, while friction resists the motion and
causes energy expenditure. River and stream flow is open channel flow.
Flows in sanitary sewers and stormwater drains are open channel flow,
except in force mains, where the water is pumped under pressure.
The key to solving routine stormwater and sanitary sewer problems
is a condition known as steady uniform flow ; that is, we assume steady
uniform flow. Steady flow, of course, means that the discharge is con-
stant with time. Uniform flow means that the slope of the water surface
and the cross-sectional flow area are also constant. It is common prac-
tice 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 flow conditions, is the same
as the slope of the channel bottom. The hydraulic grade line (HGL) lies
along the water surface, and, as in pressure flow in pipes, the HGL slopes
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