Page 398 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 325

V 2 Energy Water
2g gradient surface

D H H e Channel
bottom

Z
Datum plane

FIGURE 12.19 Energy of open-channel fluid flow.
Nonuniform flow occurs in open channels with gradual or sudden changes
in the cross-sectional area of the fluid stream. The terms gradually varied flow
and rapidly varied flow are used to describe these two types of nonuniform
flow. Equations are given next for flow in (1) rectangular cross-sectional chan-
nels, (2) triangular channels, (3) parabolic channels, (4) trapezoidal channels,
and (5) circular channels. These five types of channels cover the majority of
actual examples met in the field. Figure 12.19 shows the general energy rela-
tions in open-channel flow.

Rectangular Channels
In a rectangular channel, the critical depth D equals the mean depth D ; the
c
m
bottom width of the channel b equals the top width T; and when the discharge
of fluid is taken as the flow per foot (meter) of width q of the channel, both b
and T equal unity. Then V , the average velocity, is
c
(12.93)
V c gD c
2
and D c V c (12.94)
g
Also, Q g bD c 3/2 (12.95)
where g acceleration due to gravity in USCS or SI units.
3/2
q g D c (12.96)
3 q 2
and D c (12.97)
B g
The minimum specific energy is
3 (12.98)
H m 2 D c