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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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Presentation Transcript
outline
Outline
  • Introduction and Applications
  • Historical background
  • New Formulations
  • Conclusions
longitudinal advection vertical or lateral diffusion
Longitudinal ADVECTION+Vertical or Lateral DIFFUSION=

Dispersion Coefficient (K)

DISPERSION

practical applications
Practical Applications
  • Pollution Forecasting
  • Temperature Variations in a River
  • River Water Quality Control
  • Re-aeration in Water Bodies
  • Salt Intrusion in Tidal Estuaries
historical background
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

comparison of formulae
Comparison of Formulae

Discrepancy Ratio

Accuracy

new formulation

Seo & Cheong (1998)

New Formulation
  • Dimensional Analysis:

Factors influencing dispersion

seo cheong 1998
Seo & Cheong (1998)

Buckingham PI Theorem

simplifications
Simplifications
  • Neglect irregularities
  • Flow is fully turbulent

Reduced equation:

regression analysis
Regression Analysis

Nonlinear Multi-Regression Equation

Linear Multiple Form

final equation
Final Equation:

Experimental data:

  • 59 streams, 26 states in US
  • 35 used to model equation
  • 24 used for verification
seo cheong 19981
Seo & Cheong (1998)

Accuracy: 79%

Limitation:

deng et al 2002
Deng et al. (2002)
  • Lateral Dispersion Coefficient
  • Velocity Deviation Parameter
  • Channel Shape Equation
  • Local Flow Depth
  • Channel Sinuosity
conclusions
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).
conclusions1
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.
references
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.
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