5.9.6 PROBLEM 6 At-A-Station and Downstream Hydraulic Geometry
Relationships (English)
At bankfull discharge conditions Q1 = 8000 cfs and the width of a sand-bed stream (Ds1 = 0.6
-4
mm) is W1 = 250 ft, the maximum flow depth is yo1 = 8 ft m, the slope is Sf1 = 2.5 x 10 , and
the maximum velocity is V1 = 5 ft/s.
(a) Estimate the width, W2, depth yo2, slope Sf2 and velocity V2 at the same station when the
discharge Q2 is 200 cfs 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
200
W2 = W1 2
= 250
= 96 ft
Q
8000
1
For depth:
0.40
0.40
Q
1
= y o1 2
=8
= 1.8 ft
y o2
Q
40
1
Slope is unchanged:
S f1 = S f2 = 2.5 x 10 -4
For velocity:
0.34
0.34
Q
1
V2 = V1 2
=5
= 1.4 ft / s
Q
40
1
(b) Using the same station as for part (a), estimate the width, W2. depth yo2, slope Sf2 and
velocity V2 in an upstream section of this stream if the bankfull discharge is 500 cfs and the
material upstream is sand (D50 = 0.6 mm)?
The "downstream" geometry relationships can be used in this case. Two types of relationships
are given in Table 5.3. The sand bed relationships are a function of discharge only, whereas
the gravel bed relationships are a function of both discharge and sediment size. Both methods
are compared in the following.
5.73
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