## 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.

 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