Study of the Effect of Discharge and Bed Roughness on the Maximum Solute Diffusion Length in a Parabolic Channel

Document Type : Research Paper


1 Ph.D Candidate, Department of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

2 Associate Professor, Department of Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

3 Professor, Agricultural Engineering Research Institute, Karaj, Iran

4 Professor, Department of Water Engineering, Faculty of Agriculture, Isfahan University of Technology, Isfahan, Iran

5 Assistant Professor, Construction and Environmental Engineering Department, University of Napoli Federico II, Napoli, Italy


Diffusion processes of contaminants are important processes in channel because of their  effect on environmental pollution and health. In the present research, the effect of different levels of bed roughness coefficient and discharge rate on transverse diffusion coefficient and on the maximum solute diffusion length was studied in a non-rectangle channel. Three levels of bed roughness coefficient of about 0.2, 0.04 and 0.06 along with three levels of discharge of about 5, 10 and 15 L/s were tested: Sodium chloride was used as the soluble tracer. It was injected in to  the water at the upstream cross section. In the water tracer concentration as well as the velocity profile were mined at eight cross sections of 3, 4, 5, 6, 7, 8, 9, 9.5 meter from upstream. The results indicated that the values of the transverse diffusion coefficient varied between 0.23 and 0.56 (cm2/s) and diffusion length values ranged from 108 to 170 (m) for different treatments. As regards constant bed roughness coefficient, increasing the value of discharge can increase diffusion length. Therefore, in constant input flow, roughness coefficient is shown to exert  subtractive effect on diffusion lengths. The shape of channel affects the velocity profile, and this is why nonlinear equation was considered to calculate transverse mixing coefficient at different levels of bed roughness coefficient and discharge. In addition, an equation was also developed to explain the maximum diffusion length in a parabolic channel.


  1. Afzalimehr, H. and Anctil, F. (2000). Accelerating shear velocity in gravel bed channels. Journal of Hydrolgy, (45), pp 113-124.
  2. Afzalimehr, H. and Heidarpour, M. (2002).Fundamentals of open channel hydrodynamics. Arkan press, p. 383. (In Farsi)
  3. Azizpour, M. (2011). Empirical Study of the transverse diffusion coefficient of pollution in channel. Ms Thesis. Department of Irrigation & Reclamation Engineering, Faculty of Agriculture, University of Tehran.(In Farsi)
  4. Boxall, J. B. and Guymer, I. (2000). Estimating transverse mixing coefficients. Water and Maritime Engineering, (4), pp 263-275.
  5. Buschmann, M. H. (2005). New mixing-length approach for the mean velocity profile of turbulent boundary layers. Journal of Fluids Engineering, 127(2):393–396.
  6. Chau, K. (2000). Transverse mixing coefficient measurements in an open rectangular channel. Advances in Environmental Research, (4), pp 287-294.
  7. Deng, Z. (2002). Longitudinal dispersion coefficient in single-channel streams. Journal of Hydraulic Engineering, 128:901-909.
  8. Fischer, H. (1979). Mixing in Inland and Coastal Waters. Academic press, p. 302.
  9. Gualtieri, C. and Mucherino, C. (2007). Transverse turbulent diffusion in straight rectangular channels. 5th International Symposium on Environmental Hydraulics (ISEH 2007), Tempe (USA), December, p 1-8.

10. Kouchakzadeh, S., Akram, M., and Bagheri, F. (2006). Hydraulic performance of corrugated pipes and developing applied conveyance relations for corrugated pipes based on their hydraulic performance. Journal of Agriculture Engineering Research. 27(7):1-18.

11. Lau, Y. and Krishnappan, B. (1977). Transverse dispersion in rectangular channels. Journal of Hydraulic, 103:1173-1189.

12. Miller, A. and Richardson, E. (1974). Diffusion and dispersion in open channel flow. Journal of the Hydraulics Division, 100:159-171.

13. Pourabadeyi, M., Amiri tokaldany, E., and Liaghat, A. (2007). Study Effect of flow parameters on transverse diffusion coefficient of contaminant in are ctangular channel. 6th Iranian Hydraulic Conference, university of shahrekord, Shahrekord. IRAN. (In Farsi)

14. Rowinski, P. M. and Kubrak, J. (2002). A mixing-length model for predicting vertical velocity distribution in flows through emergent vegetation. Hydrological Sciences-Journal-des Sciences Hydrologiques. 47(6):893-904.

15. Rutherford, J. (1994). River mixing. John Wiley and Sons, Ltd. England, p. 347.

16. Saadatpour, A., Heidarpor, M., and Tabatabaei, S. H. (2011). Determination of complete mixing length in a rectangular flume. Iranian Water Research Journal, 5(9):11-18. (In Farsi)

17. Shirazialiyan, P. (2009). The Effect of Vegetation on Process of Dispersion of Pollution in a Rectangular channel. Ms Thesis. Department of Water Engineering, Faculty of Agriculture, Isfahan University of Technology. (In Farsi)

18. Tabatabaei, S. H., Heidarpour, M., Ghasemi, M., and Hoseinipour, E.,Z. (2013). Transverse Mixing Coefficient on Dunes with Vegetation on a Channel Wall. World Environmental & Water Resources Congress. MAY 19-23, 2013.Cincinnati. OHIO. USA.

19. Walker, W. R. and Skogerboe, G. V. (1987). Surface Irrigation: Theory and Practice. Prentice-Hall. Englewood Cliffs. New Jersey.

20. Wang, C. (2003). Experimental Research on Channel Flow with Vegetation. Ph. D dissertation. HoHai University, Nanjing, p. 150. (in Chinese)

21. West, J. R. and Cotton, A. P. (1980). Transverse diffusion for unidirectional flow in wide open channels. Proceedings Institution of Civil Engineers, (2), pp 491-498.