Determination of Longitudinal Dispersion Coefficient Involving Tracer Experiment Data

Document Type : Research Paper


1 PhD Candidate, Water Resources Engineering, Department of Irrigation & Reclamation Engineering, University of Tehran, Karaj, Iran

2 Associate Professor, Department of Irrigation & Reclamation Engineering, University of Tehran, Karaj, Iran

3 Professor, Department of Irrigation and Reclamation Engineering, University of Tehran, Karaj, Iran


Longitudinal dispersion coefficient is normally affected by many hydraulic parameters. So far three approaches namely, integral method, dye tracing filed measurements and empirical formulae have been widely employed to estimate the above mentioned coefficient in rivers and streams. In this paper a new equation of the longitudinal dispersion coefficient is devised and evaluated using an environmentally safe tracer plus the basic empirical equations. To achieve the aim, a length of 500 meters of a manmade concrete canal was chosen, to be used in carrying out the tracer tests. A set of experiments were conducted in Feb.2015, within three different mixing lengths, of: 45, 75 and 100 meters. The results show that differences of average, variance and maximum concentration between the measured vs estimated data using the lastly available equation) are equal to 79, 6, and 99 mg/lit while using the newly equation found in the present study they are respectively equal to 66, -1 and 44 mg/lit.


Main Subjects

Ahmad, Z. (2013). Prediction of longitudinal dispersion coefficient using laboratory and field data: relationship comparisons. Hydrology Research, 44(2), 362-376.
Chatwin, P. C. (1980). Presentation of longitudinal dispersion data. Journal of the Hydraulics Division, 106(1), 71-83.
Day, T. (1977). Field procedures and evaluation of a slug dilution gauging method in mountain streams. Journal of Hydrology (New Zealand), 16(2), 113-133.
Day, T. J. (1975). Longitudinal dispersion in natural channels. Water Resources Research, 11(6), 909-918.
Day, T. J., and Wood, I. R. (1976). Similarity of the mean motion of fluid particles dispersing in a natural channel. Water Resources Research, 12(4), 655-666.
Deng, Z. Q., Singh, V. P., and Bengtsson, L. (2001). Longitudinal dispersion coefficient in straight rivers. Journal of hydraulic engineering, 127(11), 919-927.
Elder, J. (1959). The dispersion of marked fluid in turbulent shear flow. Journal of fluid mechanics, 5(4), 544-560.
Elder, K., R. Kattelmann, and R. Ferguson. (1990). Refinements in dilution gauging for mountain streams. In Hydrology in mountainous regions. I - Hydrological measurements; the water cycle, IAHS Publication No. 193, International Association for Hydrological Science, Proceedings of two Lausanne Symposia, August 1990, 247–254.
Etemad-Shahidi, A., and Taghipour, M. (2012). Predicting Longitudinal Dispersion Coefficient in Natural Streams Using M5′ Model Tree. Journal of hydraulic engineering, 138(6), 542-554.
Fischer, H. B. (1967). The mechanics of dispersion in natural streams. Journal of Hydraulic Division, 93(6), 187-216.
Fischer, H. B. (1968). Dispersion predictions in natural streams. Journal of the Sanity Engineering Division, American Society of Civil Engineering, 94(5), 927-941.
Fischer, H. B. (1975). Discussion of "Simple Method for Predicting Dispersion in Streams". Journal of the Environmental Engineering Division, 101(3), 453-455.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. and Brooks, N. H. (2013). Mixing in Inland and Coastal Waters. Elsevier Academic Press, New York.
Guymer, I. (1998). Longitudinal dispersion in sinuous channel with changes in shape. Journal of hydraulic engineering, 124(1), 33-40.
Kashefipour, S. M. and Falconer, R. A. (2002). Longitudinal dispersion coefficients in natural channels. Water Research, 36(6), 1596-1608.
Leopold, L. B. and Maddock, T. J. (1953). The hydraulic geometry channels and some physiographic implications. Geological survey professionals. paper 252, United States Goverment Printing Office, Washington, 57 p.
Liu, H. (1977). Predicting dispersion coefficient of streams. Journal of the Environmental Engineering Division, 103(1), 59-69.
Moore, R.D. (2004a). Introduction to salt dilution gauging for streamflow measurement: Part 1. Streamline Watershed Management Bulletin 7(4):20–23.
Moore, R.D. (2004b). Introduction to salt dilution gauging for streamflow measurement Part II: Constant-rate injection. Streamline Watershed Management Bulletin 8(1):11–15.
Nordin, C. F., and Troutman, B. M. (1980). Longitudinal dispersion in rivers: The persistence of skewness in observed data. Water Resources Research, 16(1), 123-128.
Palancar, M. C., Aragón, J. M., Sánchez, F., and Gil, R. (2003). The determination of longitudinal dispersion coefficients in rivers. Water environment research, 324-335.
Sahay, R., and Dutta, S. (2009). Prediction of longitudinal dispersion coefficients in natural rivers using genetic algorithm. Hydrology Research, 40(6), 544–552.
Seo, I. W., and Baek, K. O. (2004). Estimation of the longitudinal dispersion coefficient using the velocity profile in natural streams. Journal of hydraulic engineering, 130(3), 227-236.
Seo, I. W., and Cheong, T. S. (1998). Predicting longitudinal dispersion coefficient in natural streams. Journal of hydraulic engineering, 124(1), 25-32.
Singh, S. K., and Beck, M. (2003). Dispersion coefficient of streams from tracer experiment data. Journal of environmental engineering, 129(6), 539-546.
Taylor, G. (1954). The dispersion of matter in turbulent flow through a pipe. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 223A, 446-468.
Zeng, Y., and Huai, W. (2014). Estimation of longitudinal dispersion coefficient in rivers. Journal of Hydro-environment Research, 8(1), 2-8.
Zhang, X., Q, X., Zhou, X., and Pang, H. (2006). An in situ method to measure the longitudinal and transverse dispersion coefficients of solute transport in soil. Journal of Hydrology, 328(3), 614-619.