River routing

For a river channel reach where the water surface cannot be assumed horizontal, the stored volume becomes a function of the stages at both ends of the reach, and not just at the downstream (outflow) end only.

In a typical reach, the different components of storage may be defined for a given instant in time as in Fig. 14.10. Again, the continuity equation (14.2) holds at any h = 7200 s. Then:

Fig. 14.8 Auxiliary curve for outflow O v. G for At = 2h.

Table 14.3 Calculations for level-pool routing

t

I

m

O

Im - O

G

m

0

0

0

2

60

30

0

30

30

4

120

90

1

89

119

6

180

150

6

144

133

8

240

210

14

196

459

10

300

270

31

239

698

12

360

330

55

275

973

14

330

345

85

260

1233

13

300

315

114

201

1434

18

270

285

138

147

1581

20

240

255

158

97

1378

22

210

225

171

54

1732

24

180

195

178

17

1749

26

150

135

180

-15

1734

28

120

135

178

-43

1391

30

90

105

173

-68

1323

32

60

75

133

-88

1535

34

30

45

152

-107

1428

36

0

15

139

-124

1304

38

0

123

-123

1181

Fig. 14.9 Results of level pool routing over a reservoir spillway.

Fig. 14.9 Results of level pool routing over a reservoir spillway.

Fig. 14.10 Storage for flow routing in a river reach.

given time but the total storage, S, is now the sum of prism storage and wedge storage. The prism storage is taken to be a direct function of the stage at the downstream end of the reach; the simple assumption ignores the effects of the slope of the water surface and takes the downstream stage and the outflow to be uniquely related, and thus the prism storage to be a function of the outflow, O. The wedge storage exists because the inflow, I, differs from O and so may be assumed to be a function of the difference between inflow and outflow (I _ O).

Three possible conditions for wedge storage are shown in Fig. 14.11: during the rising stage of a flood in the reach, I > O, and the wedge storage must be added to

Flood arriving

Flood arriving

Fig. 14.11 Storage in a river reach showing three possible wedge storage profiles for rising levels, steady flow and falling levels.

the prism storage; during the falling stage, I < O, and the wedge storage is negative to be subtracted from the prism storage to obtain the total storage. The total storage, S, may then be represented by:

0 0

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