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.
Flow Depth
0.46
0.46
Q
14
= y o1 b2
= 2.4
= 0.67 m
y o2
Sand bed:
Q
227
b1
0.40
0.4
Q
14
= y o1 b2
= 2.4
= 0.79 m
y o2
Gravel bed:
Q
227
b1
Channel width
0.46
0.46
Q
14
W2 = W1 b2
= 76
= 21.1 m
Sand bed:
Q
227
b1
-0.33
0.53
-0.33
0.53
D s2
Q
14
8
W2 = W1 b2
= 76
= 7.4 m
Gravel bed:
Q
Ds
227
0.6
b1
1
Friction slope
-0.46
-0.46
Q
14
= 2.5 x 10 -4
= 9 x 10 -4
= S f1 b2
S f2
Sand bed:
Q
227
b1
1
-0.4
-0.4
D s2
Q
14
8
= 2.5 x 10 -4
S f2 = S f1 b2
= 0.01
Gravel bed:
Q
Ds
227
0.6
b1
1
Velocity
0.08
0.08
Q
14
V2 = V1 b2
= 1.5
= 1.2 m / s
Sand bed:
Q
227
b1
.33
0.07
0.07
.33
D s2
Q
14
8
V2 = V1 b2
=1.5
= 2.9 m / s
Gravel bed:
Q
Ds
227
0.6
b1
1
The gravel bed relationships give a steeper, faster flowing and narrower channel as compared
to the sand bed relationships. Unless the sediment size is markedly different for two streams,
the resulting hydraulic geometry calculated from both sets of equations will be similar.
5.72
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