The river (left bank) has moved downvalley approximately 6,000 feet (1,829 m) in 50 years or
an average of 120 ft (36 m) per year. The narrowest point of the meander neck is about 2,500
ft (762 m). At its historical rate, this meandering channel will most likely lead to a cutoff in the
next 15 to 20 years. The estimated position of the channel is sketched in Figure 5.34.
5.9.5 PROBLEM 5 At-A-Station and Downstream Hydraulic Geometry
Relationships (SI)
3
At bankfull discharge conditions Q1 = 227 m /s and the width of a sand-bed stream (Ds1 = 0.6
-4
mm) is W1 = 76 m, the maximum flow depth is yo1 = 2.4 m, the slope is Sf1 = 2.5 x 10 , and the
maximum velocity is V1 = 1.5 m/s.
(a) Estimate the width, W2, depth yo2, slope Sf2 and velocity V2 at the same station when the
3
discharge Q2 is 5.7 m /s if the cross-sectional geometry is unknown.
The at-a-station hydraulic geometry relationships (Table 5.3) can be used when no specific
field data is available.
For width:
0.26
0.26
Q
5.7
W2 = W1 2
= 76
= 29.2 m
Q
227
1
For depth:
0.40
0.40
Q
5.7
= y o1 2
= 2.4
= 0.55 m
y o2
Q
227
1
Slope is unchanged:
S f1 = S f2 = 2.5 x 10 -4
For velocity:
0.34
0.34
Q
5.7
V2 = V1 2
= 1.5
= 0.43 m / s
Q
227
1
(b) Using the same station as for part (a), estimate the width, W2. depth yo2, slope Sf2 and
3
velocity V2 in an upstream section of this stream if the bankfull discharge is 14 m /s and the
material upstream is sand (D50 = 0.6 mm)?
5.71
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