STREAMFLOW ROUTING - Hydrology: An Introduction - page 233

Table 7.2 Application of the Muskingum channel routing method in Example 7.2

XQ i +

− X)Q e

(1

Q i Q e S S

(m 3 s − 1 ) (m 3 s − 1 ) (m 3 hs − 1 )(m 3 hs − 1 ) time (h) X = 0.1 X = 0.3 X = 0.5

0 172 139 0 143 149 156

1 250 124 79 79 137 162 187

2 438 220 172 251 241 285 329

3 736 342 306 557 382 460 539

4 1077 542 464 1021 596 703 810

5 1622 805 675 1696 887 1050 1214

6 2090 1271 818 2514 1353 1517 1681

7 2294 1684 714 3229 1745 1867 1989

8 2247 1973 442 3670 2001 2055 2110

9 2090 2169 98 3768 2161 2145 2130

10 1622 2090 − 273 3495 2044 1950 1856

11 1271 1895 − 546 2948 1833 1708 1583

12 1015 1622 − 615 2333 1561 1440 1318

13 844 1333 − 548 1785 1285 1187 1089

14 711 1077 − 428 1357 1040 967 894

15 627 891 − 315 1042 864 812 759

16 549 759 − 236 806 738 696 654

17 488 651 − 186 620 634 602 569

18 433 558 − 143 477 545 520 495

19 388 496 − 116 360 485 464 442

20 343 434 − 100 261 425 407 389

21 313 396 − 87 174 388 371 355

22 283 350 − 75 99 343 330 317

23 266 319 − 60 39 314 303 293

24 249 296 − 50 − 12 291 282 272

25 236 265 − 38 − 50 263 257 251

26 224 235 − 20 − 70 234 232 230

27 213 220 − 9 − 79 219 218 216

28 201 204 − 5 − 84 204 203 203

− −

29 192 197 4 88 196 195 194

30 182 189 − 6 − 94 188 187 186

Example 7.2. Standard application of the Muskingum method

Consider, as an illustration, the flow rates Q i and Q e for a channel reach; these are
listed in Table 7.2. Also listed are the results of the calculations required to estimate
the parameters as outlined already in Table 7.1. The values of incremental storage

S
were calculated by means of Equation (7.35), and were summed in the next column to
obtain the values of the storage S in the reach. These values can then be plotted against
XQ i + (1 − X ) Q e for different trial values of the weighting parameter X . The value