TECHNICAL NOTES
Aug 1, 1989

Response of Muskingum Equation to Step Input

Publication: Journal of Irrigation and Drainage Engineering
Volume 115, Issue 4

Abstract

Solution of the Muskingum equation for a step input function has been developed using the Laplace transform method. The solution is in agreement with a previous results, which was obtained by the author using a different method. The solution is different from the one published in the past by many others. The old solution predicts unrealistic negative outflows for small values of time. In contrast, the proposed solution is free of this or any other defect. The solution can be practically used by method of convolution to route physical floods without encountering negative outflows or violating the continuity of mass conservation. The source of error in the previous solution given by others has been pointed out.

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References

1.
Boneh, A., and Golan, A. (1979). “Instantaneous unit hydrograph with negative ordinates—possible?.” Water Resour. Res., 15(1.
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Cheng, D. K. (1977). Analysis of linear systems, Addison‐Wesley Publishing Co., Inc., Reading, Mass., 175, 234–235.
3.
Churchill, R. V. (1967). Operational mathematics. McGraw‐Hill Book Co., Inc., New York, N.Y., 9.
4.
Diskin, M. H. (1967). “On the solution of the Muskingum flood routing equation.” J. Hydrol., (5), 163–170.
5.
Gill, M. A. (1978). “Routing of floods in river channels.” Nord. Hydrol., (8), 163–170.
6.
Gill, M. A. (1985). “Use of time lag in Muskingum method of flood routing.” Proc. Multivariate Analysis of Hydrologic Processes, 4th International Hydrology Symp., 906–917.
7.
Kulandaiswamy, V. C. (1966). “A note on Muskingum method of flood routing.” J. Hydrol., (4), 273–276.
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Nash, J. E. (1959). “A note on the Muskingum flood routing method.” J. Geophys. Res., (64), 1053–1056.
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Overton, D. E. (1966). “Muskingum flood routing of upland stream flow.” J. Hydrol., (4), 185–200.
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Singh, V. P. (1988). Hydrologic systems—rainfall runoff modeling. Vol. 1, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 389–405.

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Published In

Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 115Issue 4August 1989
Pages: 736 - 738

History

Published online: Aug 1, 1989
Published in print: Aug 1989

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Authors

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Mohammad Akram Gill, Member, ASCE
Assoc. Civ. Engr., Detroit Water and Sewerage Dept., 400 Monroe, Detroit, MI 48226

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