CIVIL ENGINEERING FORMULAS

328 CHAPTER TWELVE

Trapezoidal Channels

Figure 12.22 shows a trapezoidal channel having a depth of Dcand a bottom
widthb. The slope of the sides, horizontal divided by vertical, is z. Expressing
the mean depth Dmin terms of channel dimensions, the relations for critical
depthDcand average velocity Vcare

(12.116)

and (12.117)

The discharge through the channel is then

(12.118)

Then, the minimum specific energy and critical depth are

(12.119)

(12.120)

Circular Channels

Figure 12.23 shows a typical circular channel in which the area a,top width T,
and depth Dcare

a (12.121)

d^2

4

( (^) r

1

2

sin 2 )

Dc

4 zHm 3 b 216 z^2 Hm^2  16 zHmb 9 b^2

10 z

Hm

3 b 5 zDc

2 b 4 zDc

Dc

Q

B

g

(bzDc)^3

b 2 zDc

D3/2c

Dc

Vc^2

c



b

2 z



B

V^4 c

g^2



b^2

4 z^2

Vc

B

bzDc

b 2 zDc

gDc

d/2

θ θ

d/2

T Dc

FIGURE 12.23 Circular channel.

Dc

z =

e

Dc

b

e e

T

FIGURE 12.22 Trapezoidal open channel.