Dispersion Equation Different Forms

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Dispersion Equation Different Forms
General Equation Plume with Reflection for
Stack Height H
Ground Level Concentration Stack at Height H
Ground Level Center Line Concentration Stack at
Height H
Ground Level Center Line Ground Point Source
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Calculation of Effective Stack Height
Note that H hs ?h, where ?h is the stack
rise. Stack rise is dependant on stack
characteristics, Meteorology, and
physico-chemical nature of effluent.
Carson-Moses Equation
Holland Formula
Concawe Formula
Where
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Preferred Equation for Stack Rise

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Wind Velocity U for the Model

• U f(z) given by (U/U1) (z/z1)p, where p
  depends on on atmospheric stability.
• Appropriate value of U for dispersion model is
  the mean value through the plume.
• If mean U is unavailable, use appropriate U at
  stack height. In most cases only U10m is
  available- then correct for U at stack height
  using above equation.
• If no mention of height of measurement of U is
  made use U as mean. If measured height is
  specified for U, then correct for it to get U at
  stack height.

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Estimating Emission Rate Q for Various Scenarios
(Ref A Kumar, Pollution Engineering, p 52,
February (1996)
Accidental Release of Low volatile liquid from a
tank on ground
Accidental Release of Highly Volatile Liquid from
Tank on Ground
Accidental Release of Heavier-than-air gas from a
tank on ground
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Concentration Isopleths
Concentration / ?g.m-3
0
0
Downwind distance / meters
Concentration isopleths
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Model of flow around a sharp edged 3-D building
in a deep boundary layer
Reattachment lines on sides and roof
Incident wind profile
Lateral edge and elevated vortex pair
Cavity zone
Turbulent wake
Mean cavity reattachment line
Separation lines and Horseshoe vortex system
Length L, Width W, Height H
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Cavity Length for Short and Long Buildings
Short Buildings
Long Buildings
Note For long buildings, independent of L/H.
Maximum height of cavity
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Effective stack height with buildings
1. Correction for stack-induced downwash
2. Building induced downwash
- stack induced downwash is first determined,
then building effect is appended
Let ?b be the smaller of H or W
If hs gt H 1.5 ?b, ? hs hs
If hs lt H ? hs hs 1.5 ?b
If H lths ? hs 2hs (H 1.5 ?b)
3. Entrained plumes
If hs gt ?b, plume remains aloft. If hs lt ?b,
plume trapped in cavity and treat as ground
level source with area ?b2.
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Effective stack height with buildings continued.
4. Plume buoyancy effect
If plume is air (mostly) and Tplume same as Tamb
? hs hs

• If not calculate density difference ?
  (Me/Ma)(Ta/Te) 1
• Where a is air and e is effluent.
• lt 0 ? standard procedure for hs
• gt 0 ? other procedures used.

5. Downwind concentration far from the stack
Use usual formula from dispersion model.
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Concentration in Cavity Wake.
More appropriate (takes bldg. dim. into account)
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Concentration immediately downwind of wake cavity
For trapped plumes consider source as ground
level
For other cases
where
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Obtaining ?y and ?z
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Stability Classes
Note that both ?y and ?z can be obtained from
Tables 4-1 and 4-2 of the textbook (Wark, Warner
and Davis Air Pollution, 3rd edition)
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EPA Air Quality and Dispersion Models
http//www.epa.gov/scram001/tt22.htm