Improved Estimates of Kinematic Wave Parameters for Circular Channels

Document Type: Research Papers


1 Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran,

2 Department of Civil Engineering, Ryerson University, Toronto, ON, Canada M5B 2K3


The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular channels were developed using the kinematic sensitivity indicator. Using this indicator, the parameters were mathematically derived nearly independent of the flow depth for two cases: constant and variable Manning’s roughness coefficients. The proposed parameters were estimated for a practical range of water depth levels and were verified using an approximate method. The results showed that the proposed parameters are more accurate than existing parameters in estimating the discharge for circular channels. The proposed parameters also improved the estimate of travel time in circular channels, which is of significant importance in drainage design.


Akgiray, O. (2004). “Simple formulae for velocity, depth of flow, and slope calculations in partially filled circular pipes”, Environmental Engineering Science, 21(3), 371-385.

American Society of Civil Engineers and Water Environment Federation (1992). “Design and construction of urban stormwater management systems”, ASCE Manual and Reports of Engineering  Practice, No. 77. New York, N.Y. 

Benefield, L.D., Judkins, J.F. and Paar, A.D. (1984). “Treatment plant hydraulics for environmental engineers”, Prentice-Hall, Englewood Cliffs, N.J.

Camp, T.R. (1946). “Design of sewers to facilitate flow”, Sewage Works Journal, 18(1), 3-16.

Chow, V.T. (1959). “Open channel hydraulics”, McGraw-Hill, New York.

Chow, V.T., Maidment, D. and Mays, L.W. (1988). “Applied hydrology”, McGraw-Hill, New York.

Christensen, B.A. (1984). “Discussion of Flow velocities in pipelines”, Journal of Hydraulic Engineering, 110(10), 1510–1512.

Hager, W.H. (1989). “Discussion of Noncircular sewer”, Journal of Environmental Engineering, 115(1), 274–276.

Haltas, I. and Kavvas, M.L. (2009). “Modeling the kinematic wave parameters with regression methods”, Journal of Hydrological Engineering, 14(10), 1049-1058.

Harley, B.M., Perkins, F.E. and Eagleson P.S. (1970). “A modular distributed model of catchment dynamics”, Report No. 133. Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Cambridge, MA.

Jain, S.C. (2001). Open channel flow, John Wiley and Sons, New York.

Lighthill, M.J. and Whitham, C.B. (1955). “On kinematic waves: Flood movement in long rivers”, Proceedings of Royal Society (London), Series A, 229, 281-316.

MacArthur, R.C. and DeVries, J.J. (1993). “Introduction and application of kinematic wave routing techniques using HEC-1”, Training Document 10, U.S. Army Corps of Engineers.

Subramanya, K. (1997). “Flow in open channels”, Tata McGraw-Hill, New Delhi.

Vatankhah,A., Kouchakzadeh, S. and Hoorfar, A.(2008). “Developing effective sensitivity indicator for irrigation network components”, International Journal of Applied Agricultural Research, 3(1) 17-36.

Wong, T.S.W. and Zhou M.C. (2006). “Kinematic wave parameters for trapezoidal and rectangular channels”, Journal of Hydrologic Engineering, 11(2), 173-183.

Wong, T.S.W. and Zhou, M.C. (2003) “Kinematic wave parameters and time of travel in circular channel revisited”, Advances in Water Resources, 26(4), 417-425.