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 Calculation of Effective Stack Height

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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

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

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.
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:

Concentration Isopleths

Concentration / g.m-3

0

0

Downwind distance / meters

Concentration isopleths

Incident wind

profile

Reattachment lines on sides and roof

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

Cavity Length for Short and Long Buildings

Short Buildings:

Long Buildings:

Note: For long buildings, independent of L/H.

Maximum height of cavity:

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’ > H + 1.5 b,  hs” = hs’

If hs’ < H  hs” = hs’ – 1.5 b

If H <hs’  hs” = 2hs’ – (H + 1.5 b)

3. Entrained plumes:

If hs” > b, plume remains aloft.

If hs” < b, plume trapped in cavity and treat as ground level

source with area b2.

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.
• < 0  standard procedure for hs
• > 0  other procedures used.

5. Downwind concentration far from the stack:

Use usual formula from dispersion model.

Concentration in Cavity Wake.

More appropriate (takes bldg. dim. into account):

Concentration immediately downwind of wake cavity

For trapped plumes consider source as ground level:

For other cases:

where

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)

EPA Air Quality and Dispersion Models

http://www.epa.gov/scram001/tt22.htm