Page 401 - Civil Engineering Formulas

328 CHAPTER TWELVE

Trapezoidal Channels
Figure 12.22 shows a trapezoidal channel having a depth of D and a bottom
c
width b. The slope of the sides, horizontal divided by vertical, is z. Expressing
the mean depth D in terms of channel dimensions, the relations for critical
m
depth D and average velocity V are
c
c
b zD c
V c gD c (12.116)
Bb 2zD c
2 4 2
V c b V c b
and D c (12.117)
c 2z B g 2 4z 2
The discharge through the channel is then
(b zD c ) 3
Q g D c 3/2 (12.118)
B b 2zD c
Then, the minimum specific energy and critical depth are

3b 5zD c
H m D c (12.119)
2b 4zD c
2
2
4zH m 3b 2 16z H m 16zH m b 9b 2
D c (12.120)
10z
Circular Channels
Figure 12.23 shows a typical circular channel in which the area a, top width T,
and depth D are
c
d 2 1
a ( r sin 2 ) (12.121)
4 2

T d/2 d/2
e e
θ θ
D c e
b z = T D c
D c
FIGURE 12.22 Trapezoidal open channel. FIGURE 12.23 Circular channel.