CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 325

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
andrapidly varied floware 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) parabolicchannels, (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 Dcequals the mean depth Dm; the
bottom width of the channel bequals the top width T; and when the discharge
of fluid is taken as the flow per foot (meter) of width qof the channel, both b
andTequal unity. Then Vc, the average velocity, is

(12.93)

and (12.94)

Also, (12.95)

wheregacceleration due to gravity in USCS or SI units.

(12.96)

and (12.97)

The minimum specific energy is

Hm^3  2 Dc (12.98)

Dc

B

(^3) q 2
g
qgDc3/2
QgbDc3/2
Dc
Vc^2
g
VcgDc

V^2

2 g

Energy

gradient

Water

surface

Channel

bottom

D H He

Z

Datum plane

FIGURE 12.19 Energy of open-channel fluid flow.