Estimating the river dispersion coefficient, Ex also called El

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Estimating the river dispersion coefficient, Ex
(also called El)

• Experimental
• Observe Ex with a dye study (recall the
  dispersed plug flow experiment in ENVE3002 and
  the dispersion model Chp 13 in Levenspiel) Sample
  problem 2.6
• Empirical
• Correlate Ex with river parameters that may be
  affecting it (recall the dispersion coefficients
  in air as a function of distance and stability
  class)

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Dye (tracer) studies

• Method of moments (review ENVE3002 notes).
• Peak concentration observed for pulse input.

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Dispersion model

• You will study the advection-dispersion equation
  (5 and 6) in detail in the contaminant transport
  course next term.

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• The solution to this equation was presented in
  the non-dimensional coordinates E? vs ? where

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Fig. 13.4
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Determination of the vessel dispersion number

• Compare experimental E? vs ? curve with the
  solution in Fig 13.4 to get the D/uL parameter by
  one of the following methods
• - by calculating its variance
• by measuring its maximum height

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One-shot tracer input (arbitrary shape)

• The additivity of variances enables us to use
  tracer inputs of arbitrary shape and use the
  difference in variance to quantify the
  dispersion Fig. 13.6
• For small extents of dispersion (D/uL lt 0.01) we
  can also use
• However, if the tracer curve shapes are very
  different from symmetrical and D/uLgt0.01 the
  models basic assumptions begin to fail. Using
  an alternate model (tanks in series?) may be a
  better idea.

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Figure 13.6
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(Fig. E14.2)
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• What is the dispersion coefficient (D, now called
  Ex or El in the river case) in Example 14.2 by
  the method of moments?
• Lets assume the 10.5 hr and 14 hr values quoted
  for the spread represent 2? values

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Peak concentration for tracer study
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