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Formulations of Longitudinal Dispersion Coefficient

A Review:. Formulations of Longitudinal Dispersion Coefficient. Outline. Introduction and Applications Historical background New Formulations Conclusions. Longitudinal ADVECTION + Vertical or Lateral DIFFUSION =. Dispersion Coefficient (K). DISPERSION. River Mixing Processes.

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Formulations of Longitudinal Dispersion Coefficient

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  1. A Review: Formulations ofLongitudinal Dispersion Coefficient

  2. Outline • Introduction and Applications • Historical background • New Formulations • Conclusions

  3. Longitudinal ADVECTION+Vertical or Lateral DIFFUSION= Dispersion Coefficient (K) DISPERSION

  4. River Mixing Processes

  5. Practical Applications • Pollution Forecasting • Temperature Variations in a River • River Water Quality Control • Re-aeration in Water Bodies • Salt Intrusion in Tidal Estuaries

  6. Historical Background • Taylor (1953 & 1954) • Elder (1959) • Fischer (1966 & 1975) • Liu (1977) • Iwasa and Aya (1991) • Taylor (1953 & 1954) • Elder (1959) • Fischer (1966 & 1975) • Liu (1977) • Iwasa and Aya (1991) Laminar flow in a tube of radius a Turbulent flow in a pipe of radius a

  7. Comparison of Formulae Discrepancy Ratio Accuracy

  8. Accuracy Comparison

  9. Seo & Cheong (1998) New Formulation • Dimensional Analysis: Factors influencing dispersion

  10. Seo & Cheong (1998) Buckingham PI Theorem

  11. Simplifications • Neglect irregularities • Flow is fully turbulent Reduced equation:

  12. Regression Analysis Nonlinear Multi-Regression Equation Linear Multiple Form

  13. Final Equation: Experimental data: • 59 streams, 26 states in US • 35 used to model equation • 24 used for verification

  14. Seo & Cheong (1998) Accuracy: 79% Limitation:

  15. Deng et al. (2002) • Lateral Dispersion Coefficient • Velocity Deviation Parameter • Channel Shape Equation • Local Flow Depth • Channel Sinuosity

  16. Deng et al. (2002)

  17. Conclusions • Analytical solution by Taylor (1954) available for regular cross sections. • Natural streams need empirical means with field data. • Liu’s equation (1977) offers the best prediction followed by Iwasa & Aya (1991).

  18. Conclusions • Seo and Cheong’s new equation (1998) with field data from 59 streams across 26 states in the US. • Deng et al. (2002) incorporated the effect of vertical and transverse irregularities.

  19. References • Seo, I. W., and Cheong, T. S. (1998). “Predicting Longitudinal Dispersion Coefficient in Natural Streams.” J. Hydr. Engrg., ASCE, 124(1), 25-32. • Liu, H. (1977). “Predicting dispersion coefficient of streams.” J. Envir. Engrg. Div., ASCE, 103(1), 59-69. • Deng, Z.-Q., Bengtsson, L., Singh, V. P., and Adrian, D. D (2002). “Longitudinal Dispersion Coefficient in Single-Channel Streams”, J. Hydr. Engrg., ASCE, 128(10), 901-916.

  20. Q & A ?

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