The document discusses plume rise in the context of air pollution, explaining that emitted gases from stacks mix with ambient air and rise due to their buoyancy and momentum. It details several formulas used to calculate plume rise, including the modified Carson and Moses formula and Briggs' formula, with specific coefficients based on stability conditions. Additionally, the document includes objective and theory questions pertaining to the topic of plume rise.

1. L-17
Plume Rise Formulae
Air Pollution and Control
(Elective -I)

2. • Gases that are emitted from stacks are often
pushed out by fans. As the turbulent exhaust
gases exit the stack they mix with ambient air.
This mixing of ambient air into the plume is
called entrainment. As the plume entrains
air into it, the plume diameter grows as it
travels downwind. These gases have
momentum as they enter the atmosphere.
Often these gases are heated and are warmer
than the outdoor air. In these cases the emitted
gases are less dense than the outside air and
are therefore buoyant.
Prof S S Jahagirdar, NKOCET
2

3. • A combination of the gases' momentum and
buoyancy causes the gases to rise. This is
referred to as plume rise and allows air
pollutants emitted in this gas stream to be
lofted higher in the atmosphere. Since the
plume is higher in the atmosphere and at a
further distance from the ground, the plume
will disperse more before it reaches ground
level.
Prof S S Jahagirdar, NKOCET
3

4. Plume Rise
>
hs= Physical Stack height
H= Effective stack height
Prof S S Jahagirdar, NKOCET
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5. Buoyancy =Plume rise
<
5
Prof S S Jahagirdar, NKOCET

6. 1. IS formula
Prof S S Jahagirdar, NKOCET
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7. 2. Modified Carson and
Moses formula
0.5
h  a.[(Vs .d ) / u ]  b.[(Qh ) / u ]
Stability
Condition
a
b
Unstable
3.47
0.35
-1.04
5.15
2.64
2.24
Neutral
Stable
Prof S S Jahagirdar, NKOCET
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8. Prof S S Jahagirdar, NKOCET
8

9. 3. Holland’s Formula
Ts= Stack gas temperature in 0 K
Ta =Ambient air temperature in 0 K
Prof S S Jahagirdar, NKOCET
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10. 4. Concave formula
1/ 2
h
h  2.71[Q
3/ 4
/u ]
It is modified by Thomas
h  4.71[Q
0.444
Prof S S Jahagirdar, NKOCET
/u
0.694
]
10

11. 5. Brigg’s formula
1/3
h  114.C.( F )
/u
2
g .Vs .d .(Ts  Ta )
F
4.Ta
  
C  1.58  41.4 

 z 
Prof S S Jahagirdar, NKOCET
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12. • F= Flux (m4/Sec3)
• G= gravitational acceleration.
•    = potential temperature gradient
 z 
  (Similar to dT/dZ)
Prof S S Jahagirdar, NKOCET
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13. 6. Davidson and Bryant
formula
Vs 
h  d .

 u 
1 .4

T 
. 1 

Ts 

Where,
Ts-Ta= T
Prof S S Jahagirdar, NKOCET
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14. Objective Questions
1. Plume rise is measures from top of the stack and
is measured up to
____________________________.
2. Stack gas temperature is ___________ than the
surrounding air.
3. IS: _______ suggested plume rise formula based
on Brigg’s equation.
4. Values of coefficients a and b in case of modified
Carson and Moses equation for unstable stability
class are ____ and ____ respectively. (Similar
questions for other Stwo stability categories.) 14
Prof S Jahagirdar, NKOCET

15. 5. Plume rise is due to _________________ and
_______________.
6. Effective stack height =
________________+____________________.
7. True or False?
Plume rise (Δh) is the height that pollutants rise
above a stack and is measured from the top of
the stack to the upper edge of the plume.
Prof S S Jahagirdar, NKOCET
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16. Theory Questions
Q1. Explain what is ‘Plume rise’. Give any three
formulae for the same.
Q2. Give IS formula for plume rise.
Prof S S Jahagirdar, NKOCET
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17. Go to Problems
Prof S S Jahagirdar, NKOCET
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