TEMPERATURE LAPSE RATE THE STANDARD ATMOSPHERE

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PLUME RISE

• H h ??h
• h physical stack height, ?
• ?h plume rise due to thermal buoyancy and
  momentum
• Correlations of various complexity exist between
  plume rise, stack temperature, stack velocity,
  atmospheric conditions etc. (e.g. Hollands,
  equation 6.35 de Nevers)

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PLUME RISE - HOLLANDS EQUATION
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PLUME RISE - BUOYANCY AND MOMENTUM FLUXES
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Table 4-6 Wark, Warner Davis

• Equations for calculating final plume rise

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STACK TIP DOWNWASH

• For Vs lt 1.5 us
• (Vs stack gas velocity, us wind velocity at stack
  height)
• Note that maximum downwash correction is 3 stack
  diameters

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BUILDING DOWNWASH AND WAKE EFFECTS

• Figs. 3-19 and 3-20 demonstrate these. Special
  treatments are included in models.
• BUILDING DOWNWASH - Simple rule of thumb
•   downwash unlikely to be a problem if
• hs ? hb 1.5 Lb
•  hs stack height
• hb building height
• Lb the lesser of either building height or
  maximum projected building width.
• Good Engineering Practice (GEP) rule for stack
  design.
•  

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LINE SOURCES - Infinite line source

• Can be handled in principle as one dimensional
  dispersion from a point source.
• For wind perpendicular to line source
• q emission per unit time per unit distance

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Oblique wind and finite line source

• For wind at an angle of ? with the line source,
  the strength is effectively increased by a
  factor of
• (sin ? )-1
• For a finite line source we must consider the end
  effects, the resulting concentration will be less
  than that for an infinite line source under the
  same conditions.
• Examples 4-9 and 4-10 (Wark, Warner Davis)
  demonstrate the application of the infinite line
  source case to CO concentrations near a highway.

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COMPLICATIONS

• For ? lt 45, the (sin ? )-1 correction becomes
  increasingly inaccurate.
• The dispersion due to vehicle induced turbulence
  and thermal buoyancy due to heat release from
  the vehicles are important factors
• The P-G-T dispersion coefficients were originally
  observed in flat grass terrain, most highways of
  interest have some roughness effects associated
  with them (bridge, below grade. above grade etc.)

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CALINE

• series of models developed to provide better
  estimations of motor vehicle pollutant
  concentrations near highways and arteries.
• Main features
• - Finite line segment approach
• - Mixing zone concept to incorporate traffic
  induced dispersion
• - New dispersion data near highways,
  adjustments for averaging time and surface
  roughness included for P-G-T coefficients

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3 DIMENSIONAL DISPERSION MODEL

• Similar to heat conduction equation in 3-d
• Solution for instantaneous release of X g of
  pollutant at t 0 and x y z 0

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PUFF RELEASE

• Solution for instantaneous release of X g of
  pollutant at t 0 and (x0, y0, z0)
• Using ? instead of K, we get

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PUFF RELEASE

• To consider ground reflection we add a virtual
  source below the ground at (x0, y0, -z0) that is
  the mirror image of the real source above the
  ground.

Virtual source to account for reflection
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• At z 0 (cwith reflection ) 2(cwithout
  reflection )
• Not as simple at other z.

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PUFF RELEASE

• Say we release a puff at ground level (z00)
• The center of the plume (y00) is travelling in
  the x direction with windspeed u, i.e. x0 ut
• Ground-level concentration (z0) along the center
  line of the plume, y0 , will be given by

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PUFF RELEASE

• Ground-level concentration will be at a maximum
  for xx0 i.e

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Decay of pollutants in the atmosphere

• The mass balances we have used so far assume
  conservative pollutants no generation or
  consumption terms.
• For a reactant being consumed by a first order
  reaction in a batch reactor

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Decay of pollutants in the atmosphere

• The time spent in the atmosphere after release
  x/u
• Thus, first order decay in the atmosphere can be
  modelled simply by

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ATMOSPHERIC TURBULENCE AND SAMPLING TIME

• The time scale for atmospheric turbulence can be
  quite long, of the order of many minutes.
• Field observations of dispersion coefficients are
  specific to the sampling (averaging) time used
  (typically 10 minutes)
• Estimates of corrections for other sampling
  periods can be made

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• From Air Dispersion Modelling Guideline for
  Ontario, Guidance for Demonstrating Compliance
  with The Air Dispersion Modelling Requirements
  set out in Ontario Regulation 419/05, Air
  pollution Local Air Quality, made under the
  Environmental Protection Act, July 2005.
• Available at http//www.ene.gov.on.ca/envision/ai
  r/regulations/localquality.htm