Section 5 Consequence Analysis 5.1 Dispersion Analysis

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Section 5 Consequence Analysis5.1 Dispersion
Analysis
Process Control Safety Group Institute of
Hydrogen Economy Universiti Teknologi
Malaysia Dr. Arshad Ahmad Email
arshad_at_cheme.utm.my
www.utm.my
innovative ? entrepreneurial ? global
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Accident Happens

• Spills of materials can lead to disaster
• toxic exposure
• Fire
• explosion
• Materials are released from holes, cracks in
  various plant components
• Tanks, pipes, pumps
• Flanges, valves,

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Source Model
Arshad Ahmad Professor of Process Control
Safety Director, Institute of Hydrogen Economy,
UTM
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Various types of limited aperture releases.
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Release Mechanism

• Wide Aperture
• Release of substantial amount in short time
• example Overpressure of tank and explosion
• Limited Aperture
• Release from cracks, leaks etc
• Relief system is designed to prevent over-pressure

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Source Models

• Source models represent the material release
  process
• Provide useful information for determining the
  consequences of an accident
• rate of material release, the total quantity
  released, and the physical state of the material.
• valuable for evaluating new process designs,
  process improvements and the safety of existing
  processes.

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Release of Gasses
Gasses/vapours Disperse to atmosphere
Gas / Vapour Leak
Gas / Vapour
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Release of Liquids
Gasses/vapours Disperse to atmosphere
Vapour or Two Phase Liquid
Vapour
Liquid

• Liquid flashes into vapour
• Liquid collected as in a pool

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Basic Models

1. Flow of liquids through a hole
2. Flow of liquids through a hole in a tank
3. Flow of liquids through pipes
4. Flow of vapor through holes
5. Flow of vapor through pipes
6. Flashing liquids
7. Liquid pool evaporation or boiling

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Mechanical Energy Balance
General mechanical energy balance Equation
(1)

• P is the pressure (force/area),
• r is the fluid density (mass/volume)
• u is the average instantaneous velocity of the
  fluid (length/time)
• gc is the gravitational constant (length
  mass/force time²),
• a is the unitless velocity profile correction
  factor - (0.5 for laminar flow, 1.0 for plug
  flow, gt1.0 for turbulent flow)
• g is the acceleration due to gravity
  (length/time²)
• z is the height above datum (length)
• F is the net frictional loss term (length
  force/mass)
• Ws is the shaft work (force length)
• m is the mass flow rate (mass/time)

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Mechanical Energy Balance
Typical Simplifications

• Incompressible Fluid
• Density is constant
• No elevation difference (Dz 0)
• No shaft work, Ws 0
• Negligible velocity change (small aperture), Du
  0

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1. Flow of Liquid Through Holes
(2)
Liquid escaping through a hole in a process unit.
The energy of the liquid due to its pressure in
the vessel is converted to kinetic energy with
some frictional flow losses in the hole.
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Discharge Coefficients

• The following guidelines are suggested to
  determine discharge coefficients
• For sharp-edged orifices and for Reynolds number
  greater than 30,000, Co approaches the value
  0.61. For these conditions, the exit velocity of
  the fluid is independent of the size of the hole.
• For a well-rounded nozzle the discharge
  coefficient approaches unity.
• For short sections of pipe attached to a vessel
  (with a length-diameter ratio not less than 3),
  the discharge coefficient is approximately 0.81.
• For cases where the discharge coefficient is
  unknown or uncertain, use a value of 1.0 to
  maximize the computed flows.

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2. Flow of Liquid Through a Hole in a Tank
A hole develops at a height hL below the fluid
level. The flow of liquid through this hole is
represented by the mechanical energy
balance assumptions fluid is incompressible, he
shaft work, Ws is zero and the velocity of the
fluid in the tank is zero.
The mass discharge rate at any time t. The
time for the vessel to empty to the level of the
leak, te, is
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3. Flow of Liquid Through Pipes

• A pressure gradient across the pipe is the
  driving force
• Frictional forces between the liquid and the wall
  of the pipe converts kinetic energy into thermal
  energy. This results in a decrease in the liquid
  velocity and a decrease in the liquid pressure.

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Summation of Friction Elements
The friction term, F, is the sum of all of the
frictional elements in the piping system. For a
straight pipe, without valves or fitting, F is
given by (12) where ƒ is the Fanning friction
factor (no units) L is the length of the pipe d
is the diameter of the pipe (length)
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Fanning Friction Factor

• The Fanning friction factor, ƒ, is a function of
  the Reynolds number, Re, and the roughness of the
  pipe, e.
• For laminar flow, the Fanning friction factor is
  given by
• For turbulent flow, the data shown in Figure 6
  are represented by the Colebrook equation
• Refer to Figure 6 and roughness in Table 1

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Roughness
Table 1 Roughness factor, e, for clean pipes.
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Fanning Friction Factor
Figure 6 Plot of Fanning friction factor, f,
versus Reynolds number
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Figure 7 Plot of 1/? ƒ, versus Re ? ƒ. This form
is convenient for certain types of problems. (see
Example 2.)
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Fittings, elbows etc

• For piping systems composed of fittings, elbows,
  valves, and other assorted hardware, the pipe
  length is adjusted to compensate for the
  additional friction losses due to these fixtures.
  The equivalent pipe length is defined as
• The summation of all of the valves, unions,
  elbows, and so on, are included in the
  computation of overall piping equivalent length
  (see Table 2))

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Table 2 Equivalent pipe lengths for various pipe
fittings (Turbulent flow only).
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Table 2 Equivalent pipe lengths for various pipe
fittings (Turbulent flow only)- contd
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4. Flow of Vapour Through Holes

• For flowing liquids the kinetic energy changes
  are frequently negligible and the physical
  properties (particularly the density are
  constant.
• For flowing gases and vapor these assumptions are
  only valid for small pressure changes (P1/P2 lt
  2)and low velocities ( 0.3 speed of sound in
  gas).
• Gas and vapor discharges are classified into
  throttling and free expansion releases.
• For throttling releases, the gas issues through a
  small crack with large frictional losses very
  little of energy inherent with the gas pressure
  is converted to kinetic energy.
• For free expansion releases, most of the pressure
  energy is converted to kinetic energy the
  assumption of isentropic behavior is usually
  valid.
• Source models for throttling releases require
  detailed information on the physical structure of
  the leak they will not be considered here. Free
  expansion release source models require only the
  diameter of the leak.

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Figure 9 A free expansion gas leak. The gas
expands isentropically through the hole. The gas
properties (P, T) and velocity change during the
expansion
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Flow of Vapour Through Holes

• The resulting equation is
• The maximum flowrate is at the choke,

Here
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5. Flow of Vapour Through Pipes

• Vapor flow through pipes is modeled using two
  special cases adiabatic or isothermal behavior.
  
• The adiabatic case corresponds to rapid vapor
  flow through an insulated pipe.
• The isothermal case corresponds to flow through
  an uninsulated pipe maintained at a constant
  temperature an underwater pipeline is an
  excellent example.
• Real vapor flows behave somewhere between the
  adiabatic and isothermal cases.

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Adiabatic Flows
An adiabatic pipe containing a flowing vapor is
shown in Figure 11. For this particular case the
outlet velocity is less than the sonic velocity.
The flow is driven by a pressure gradient across
the pipe. This expansion leads to an increase in
velocity and an increase in the kinetic energy of
the gas. The kinetic energy is extracted from the
thermal energy of the gas a decrease in
temperature occurs. However, frictional forces
are present between the gas and the pipe wall.
These frictional forces increase the temperature
of the gas. Depending on the magnitude of the
kinetic and frictional energy terms either an
increase or decrease in the gas temperature is
possible.
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Figure 11 Adiabatic, non-choked flow of gas
through a pipe. The gas temperature might
increase or decrease, depending on the magnitude
of the frictional losses
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For most problems the pipe length (L), inside
diameter (d), upstream temperature (T1) and
pressure (P1), and downstream pressure (P2) are
known. To compute the mass flux, G, the procedure
is as follows. 1. Determine pipe roughness, e
from Table 1. Compute e/d. 2. Determine the
Fanning friction factor, f, from Equation 27.
This assumes fully developed turbulent flow at
high Reynolds numbers. This assumption can be
checked later, but is normally
valid. 3. Determine T2 from Equation
51. 4. Compute the total mass flux, G, from
Equation 52. For long pipes, or for large
pressure differences across the pipe, he velocity
of the gas can approach the sonic velocity. This
case is shown in Figure 12. At the sonic velocity
the flow will be choked. The gas velocity will
remain at the sonic velocity, temperature, and
pressure for the remainder of the pipe. For
choked flow, Equations 46 through 50 are
simplified by setting Ma2 1.0. The results are
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Figure 12 Adiabatic, choked flow of gas through
a pipe. The maximum velocity reached is the sonic
velocity of the gas
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For most problems involving choked, adiabatic
flows, the pipe length (L), inside diameter (d),
and upstream pressure (P1) and temperature (T1)
are known. To compute the mass flux, G, the
procedure is as follows. 1. Determine the Fanning
friction factor, f, using Equation 27. This
assumes fully developed turbulent flow at high
Reynolds number. This assumption can be
checked later, but is normally valid. 2. Determine
Ma1, from Equation 57. 3. Determine the mass
flux, Gchoked, from Equation 56. 4. Determine
Pchoked from Equation 54 to confirm operation
at choked conditions.
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Isothermal Flow
Isothermal flow of gas in a pipe with friction is
shown in Figure 13. For this case the gas
velocity is assumed to be well below the sonic
velocity of the gas. A pressure gradient across
the pipe provides the driving force for the gas
transport. As the gas expands through the
pressure gradient the velocity must increase to
maintain the same mass flowrate. The pressure at
the end of the pipe is equal to the pressure of
the surroundings. The temperature is constant
across the entire pipe length. Isothermal flow is
represented by the mechanical energy balance in
the form shown in Equation 44. The following
assumptions are valid for this case.
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Figure 13 Isothermal, non-choked flow of gas
through a pipe.
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Figure 14 Isothermal, choked flow of gas through
a pipe. The maximum velocity reached is a/??.
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For most typical problems the pipe length (L),
inside diameter (d), upstream pressure (P1), and
temperature (T) are known. The mass flux, G, is
determined using the following procedure. 1. Deter
mine the Fanning friction factor, f, using
Equation 27. This assumes fully developed
turbulent flow at high Reynolds number. This
assumption can be checked later, but is usually
valid. 2. Determine Ma1 from Equation
71. 3. Determine the mass flux, G, from Equation
70.
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6. Flashing Liquids

• Liquids stored under pressure above their normal
  boiling point will partially flash into vapour
  following a leak, sometimes explosively.
• Flashing occurs so rapidly that the process is
  assumed to be adiabatic.
• The excess energy contained in the superheated
  liquid vaporizes the liquid and lower the
  temperature to the new boiling point.

m the mass of original liquid, Cp heat
capacity of the liquid (energy/mass deg), To
temperature of the liquid prior to
depressurization Tb boiling point of the
liquid Q excess energy contained in the
superheated liquid
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Fraction of Liquid Vaporised
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7. Liquid Pool Evaporation or Boiling
The case for evaporation of volatile from a pool
of liquid has already been considered in Chapter
3. The total mass flowrate from the evaporating
pool is given by
Qm is the mass vaporization rate (mass/time), M
is the molecular weight of the pure material, K
is the mass transfer coefficient
(length/time), A is the area of exposure, Psat
is the saturation vapor pressure of the
liquid, Rg is the ideal gas constant, and TL is
the temperature of the liquid.
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Mass Dispersion Models
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Dispersion models

• Dispersion models describe the airborne transport
  of toxic materials away from the accident site
  and into the plant and community.
• After a release, the airborne toxic is carried
  away by the wind in a characteristic plume or a
  puff
• The maximum concentration of toxic material
  occurs at the release point (which may not be at
  ground level).
• Concentrations downwind are less, due to
  turbulent mixing and dispersion of the toxic
  substance with air.

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Plume
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Puff
Wind Direction
Concentrations are the Same on All Three Surfaces
Puff at time t1gt 0
Puff at time t2gt t1
Initial puff formed by Instantaneous release of
Materials
Puff moves down wind and dissipates By Mixing
with fresh air
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Factors Influencing Dispersion

• Wind speed
• Atmospheric stability
• Ground conditions, buildings, water, trees
• Height of the release above ground level
• Momentum and buoyancy of the initial material
  released

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Wind speed

• As the wind speed increases, the plume becomes
  longer and narrower the substance is carried
  downwind faster but is diluted faster by a larger
  quantity of air.

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Atmospheric stability

• Atmospheric stability relates to vertical mixing
  of the air.
• During the day the air temperature decreases
  rapidly with height, encouraging vertical
  motions.
• At night the temperature decrease is less,
  resulting in less vertical motion.
• Temperature profiles for day and night situations
  are shown in Figure 3.
• Sometimes an inversion will occur. During and
  inversion, the temperature increases with height,
  resulting in minimal vertical motion. This most
  often occurs at night as the ground cools rapidly
  due to thermal radiation.

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Figure 3 Day Night Condition
Air temperature as a function of altitude for day
and night conditions. The temperature gradient
affects the vertical air motion.
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Ground conditions

• Ground conditions affect the mechanical mixing at
  the surface and the wind profile with height.
  Trees and buildings increase mixing while lakes
  and open areas decrease it. Figure 4 shows the
  change in wind speed versus height for a variety
  of surface conditions.

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Figure 4 Effect of Ground Condition
Effect of ground conditions on vertical wind
gradient.
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Height of the release above ground level

• The release height significantly affects ground
  level concentrations.
• As the release height increases, ground level
  concentrations are reduced since the plume must
  disperse a greater distance vertically. This is
  shown in Figure 5.

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Figure 5 - Effect of Release Height
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Momentum and buoyancy of the initial material
released

• The buoyancy and momentum of the material
  released changes the effective height of the
  release.
• Figure 6 demonstrates these effects. After the
  initial momentum and buoyancy has dissipated,
  ambient turbulent mixing becomes the dominant
  effect.

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Figure 6- Effect of Momentum and Buoyancy
The initial acceleration and buoyancy of the
released material affects the plume character.
The dispersion models discussed in this chapter
represent only ambient turbulence.
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Neutrally Buoyant Dispersion Model

• Estimates concentration downwind of a release
• Two types
• Plume Model
• Puff Model
• The puff model can be used to describe a plume a
  plume is simply the release of continuous puffs.

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Neutrally Buoyant Dispersion Model

• Consider the instantaneous release of a fixed
  mass of material, Qm, into an infinite expanse
  of air (a ground surface will be added later).
  The coordinate system is fixed at the source.
  Assuming no reaction or molecular diffusion, the
  concentration, C, of material due to this release
  is given by the advection equation.

(Eq 1)
where uj is the velocity of the air and the
subscript j represents the summation over all
coordinate directions, x, y, and z.
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Case 1 Steady state continuous point release
with no wind

• The applicable conditions are
• Constant mass release rate, Qm constant,
• No wind, ltujgt 0,
• Steady state, ?ltCgt/?t 0, and
• Constant eddy diffusivity, Kj K in all
  directions.

• Analytical Solution

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Case 2 Puff with No Wind
The applicable conditions are - - Puff release,
instantaneous release of a fixed mass of
material, Qm (with units of mass), - No wind,
ltujgt 0, and - Constant eddy diffusivity, Kj
K, in all directions.
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Case 2 Puff With No Wind
The initial condition required to solve Equation
17 is (18) The solution to Equation 17 in
spherical coordinates is (19) and in rectangular
coordinates is (20)
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Case 3 Non Steady State, Continuous Point
Release with No Wind
The applicable conditions are - Constant
mass release rate, Qm constant, - No wind,
ltujgt 0, and - Constant eddy diffusivity,
Kj K in all directions
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Case 4 Steady State, Continuous Point Release
with No Wind

• The applicable conditions are
• Continuous release, Qm constant,
• Wind blowing in x direction only, ltujgt ltuxgt u
  constant, and
• Constant eddy diffusivity, Kj K in all
  directions.
• For this case, Equation 9 reduces to

(23)
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Case 5 Puff with no wind. Eddy diffusivity a
function of direction
This is the same as Case 2, but with eddy
diffusivity a function of direction. The
applicable conditions are - - Puff release,
Qm constant, - No wind, ltujgt 0, and -
Each coordinate direction has a different, but
constant eddy diffusivity, Kx, Ky and Kz.
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Case 6 Steady state continuous point source
release with wind. Eddy diffusivity a function of
direction

• This is the same as Case 4, but with eddy
  diffusivity a function of direction. The
  applicable conditions are
• Puff release, Qm constant,
• Steady state, ?ltCgt/?t o,
• Wind blowing in x direction only, ltujgt ltuxgt u
  constant,
• Each coordinate direction has a different, but
  constant eddy diffusivity, Kx, Ky and Kz, and.

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Case 7- Puff with no wind

• This is the same as Case 5, but with wind. The
  applicable conditions are
• Puff release, Qm constant,
• Wind blowing in x direction only, ltujgt ltuxgt u
  constant, and
• Each coordinate direction has a different, but
  constant eddy diffusivity, Kx, Ky and Kz,.

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Case 8 Puff with no wind with source on ground
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Case 9 Steady state Plume with source on ground
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Case 10 continuous steady state source. Source
as height Ht, above the ground
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Pasquill-Gifford Model

• Dr. AA
• Department of Chemical Engineering
• University Teknology Malaysia

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Pasquill-Gifford Model

• Cases 1 through 10 described previously depend on
  the specification of a value for the eddy
  diffusivity, Kj.
• In general, Kj changes with position, time, wind
  velocity, and prevailing weather conditions and
  it is difficult to determine.
• Sutton solved this difficulty by proposing the
  following definition for a dispersion coefficient
• with similar relations given for sy and sz.
• The dispersion coefficients, sx, sy, and sz
  represent the standard deviations of the
  concentration in the downwind, crosswind and
  vertical (x,y,z) directions, respectively. Values
  for the dispersion coefficients are much easier
  to obtain experimentally than eddy diffusivities

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Table 2 Atmospheric Stability Classes for Use
with the Pasquill-Gifford Dispersion Model
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Figure 10 Horizontal dispersion coefficient for
Pasquill-Gifford plume model. The dispersion
coefficient is a function of distance downwind
and the atmospheric stability class.
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Figure 11 Vertical dispersion coefficient for
Pasquill-Gifford plume model. The dispersion
coefficient is a function of distance downwind
and the atmospheric stability class.
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Figure 12 Horizontal dispersion coefficient for
puff model. This data is based only on the data
points shown and should not be considered
reliable at other distances.
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Figure 13 Vertical dispersion coefficient for
puff model. This data is based only on the data
points shown and should not be considered
reliable at other distances.
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Table 3 Equations and data for Pasquill-Gifford
Dispersion Coefficients
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Case 11 Puff. Instantaneous point source at
ground level. Coordinates fixed at release point.
Constant wind in x direction only with constant
velocity u
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Case 12- Plume. Continuous, steady state, source
at ground level, wind moving in x direction at
constant velocity u
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Case 13 Plume. Continuous, Steady State Source
at Heignt H, above ground level, wind moving in x
direction at constant velocity u
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Case 14 Puff. Instantaneous point source at
height H, above ground level. Coordinate system
on ground moves with puff
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Case 15 Puff. Instantaneous point source at
height H, above ground level. Coordinate system
fixed on ground at release point
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End of Section 5.1