1 r0 v2
∆Z =
∆r
g ri r
Total superelevation is 0.133 feet.
Based on relationships, V = Q/A = 3.61 ft/s, the following are obtained:
Woodward's Equation 2.160
(3.61)
2
2
∆Z = V (r0 - ri) =
(513 - 350) = 0.153 ft
32.2 (431)
g rc
Ippen and Drinker's Equation 2.162
3.612
2
2W
2 x 163
1
1
∆Z = V
= 0.158 ft
=
x
2
2
2g rc W
2 x 32.2
431
163
1 - 2r
1 -
2 x 431
c
Ippen and Drinker's Equation 2.163
2
2
= 3.61 x 2 x 163
2W
1
1
V
= 0.151 ft
∆Z =
2g rc
2
2
W 2 x 32.2
431
163
1 -
1 -
2
2
12 rc
12 x 431
Combined Free and Forced Vortex Equation 2.165
Vmax = 4.90 ft/s
(V )
rc
2
2
2
2
2
2
2 - ri
4.90 2 - 350 - 431
- =
= 0.236 ft
r 2 x 32.2 431 513
max
∆Z =
r
2g
c
o
The equations give comparable results (0.133 to 0.236 ft). Equation 2.158, which integrates
across the section using the velocity distribution is the most exact. But using the value 0.24 ft
provides a safety factor.
2.15.4 PROBLEM 4 Maximum Stream Constriction Without Causing Backwater
(Neglecting Energy Losses)
A stream is rectangular in shape and 100 ft wide. The design discharge is 5,000 cfs and the
uniform depth for this discharge is 10 ft. Neglecting energy losses what is the maximum amount
of constriction that a bridge can impose without causing backwater.
2.85
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