onlinerouting04:   Muskingum routing   ⇒   S = K[XI + (1-X)O]

Formulas

O2 = C0I2 + C1I1 + C2O1            C0 = [(Δt/K) - 2X]/[2(1-X) + (Δt/K)]

C1 = [(Δt/K) + 2X]/[2(1-X) + (Δt/K)]           C2 = [2(1-X) - (Δt/K)]/[2(1-X) + (Δt/K)]

Reference

Ponce, V. M. 1989. Engineering Hydrology, Principles and Practices. Prentice Hall, pages 271-275.
Return
SAMPLE INPUT DATA:

Time interval Δt (hr):     24

Storage constant K (hr):     48

Weighting factor X :     0.1

Number of inflow hydrograph ordinates n:     24

Inflow hydrograph ordinates Qi:      352,587,1353,2725,4408.5,5987,6704,6951,6839,6207,5346,4560,3861.5,3007,2357.5,1779,1405,1123,952.5,730,605,514,422,352

SAMPLE OUTPUT:

Ratio Δt/K =   0.5

Time interval Time (hr) Time (days) Inflow C0I2 C1I1 C2O1 Outflow
0 0 0 352 - - - 352
1 24 1 587 76.565 107.13 198.957 382.652
2 48 2 1353 176.478 178.652 216.282 571.412
3 72 3 2725 355.435 411.783 322.972 1090.189
4 96 4 4408.5 575.022 829.348 616.194 2020.564
5 120 5 5987 780.913 1341.717 1142.058 3264.688
6 144 6 6704 874.435 1822.13 1845.259 4541.824
7 168 7 6951 906.652 2040.348 2567.118 5514.118
8 192 8 6839 892.043 2115.522 3116.675 6124.24
9 216 9 6207 809.609 2081.435 3461.527 6352.571
10 240 10 5346 697.304 1889.087 3590.583 6176.975
11 264 11 4560 594.783 1627.043 3491.334 5713.16
12 288 12 3861.5 503.674 1387.826 3229.177 5120.677
13 312 13 3007 392.217 1175.239 2894.296 4461.752
14 336 14 2357.5 307.5 915.174 2521.86 3744.534
15 360 15 1779 232.043 717.5 2116.476 3066.019
16 384 16 1405 183.261 541.435 1732.967 2457.663
17 408 17 1123 146.478 427.609 1389.114 1963.201
18 432 18 952.5 124.239 341.783 1109.635 1575.657
19 456 19 730 95.217 289.891 890.589 1275.697
20 480 20 605 78.913 222.174 721.046 1022.133
21 504 21 514 67.043 184.13 577.728 828.901
22 528 22 422 55.043 156.435 468.51 679.988
23 552 23 352 45.913 128.435 384.341 558.689
24 576 24 352 45.913 107.13 315.781 468.824
25 600 25 352 45.913 107.13 264.988 418.031
26 624 26 352 45.913 107.13 236.278 389.322
27 648 27 352 45.913 107.13 220.051 373.095
28 672 28 352 45.913 107.13 210.88 363.923
29 696 29 352 45.913 107.13 205.696 358.739
30 720 30 352 45.913 107.13 202.766 355.809
31 744 31 352 45.913 107.13 201.11 354.153
32 768 32 352 45.913 107.13 200.173 353.217
33 792 33 352 45.913 107.13 199.644 352.688

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