Design of Stack Height
A stack (chimney) is provided in industries and thermal power plants to discharge flue gases at a sufficient height above the ground. The purpose of providing adequate stack height is to ensure proper dispersion of pollutants into the atmosphere so that their concentration near ground level remains within permissible limits.
The Central Pollution Control Board (CPCB), New Delhi, has prescribed empirical equations for determining the minimum chimney height required for different pollutant emissions.
Importance of Stack Height
- Reduces ground-level concentration of pollutants.
- Improves atmospheric dispersion.
- Protects public health.
- Minimizes environmental impacts.
- Helps industries comply with pollution control regulations.
1. Chimney Height for Particulate Matter
For industries emitting particulate matter (dust), the required chimney height is given by:
- h = Height of chimney (m)
- Q = Particulate matter emission rate (tonnes/hour)
Example
If particulate emission = 2 tonnes/hour
h = 74(2)0.27
h ≈ 89 m
2. Chimney Height for Sulphur Dioxide (SO₂)
For industries emitting sulphur dioxide:
- h = Height of chimney (m)
- Qs = SO₂ emission rate (kg/hour)
Example
If SO₂ emission rate = 1000 kg/hr
h = 14(1000)0.3
h ≈ 111 m
Minimum Chimney Heights Specified
| Industry Type | Minimum Chimney Height |
|---|---|
| General Industries (except Thermal Power Plants) | 30 m |
| Thermal Power Plants above 200 MW and below 500 MW | 220 m |
| Thermal Power Plants above 500 MW | 275 m |
Effective Height of a Stack
The equations above actually use the effective stack height rather than the physical height of the chimney.
When hot gases leave the chimney, they continue to rise above the stack due to their momentum and buoyancy. Therefore:
- H = Effective stack height (m)
- h = Actual chimney height (m)
- Δh = Plume rise above chimney (m)
Holland's Equation for Plume Rise
One of the most commonly used equations for estimating plume rise is Holland's equation:
Meaning of Terms
| Symbol | Description | Unit |
|---|---|---|
| Δh | Plume rise | m |
| Vs | Stack gas exit velocity | m/s |
| D | Inside Exit diameter of Stack | m |
| U | Wind speed | m/s |
| P | Atmospheric pressure | millibars |
| Ts | Stack gas temperature | K |
| Ta | Ambient air temperature | K |
Atmospheric Stability Correction
- Neutral atmosphere → Use equation directly.
- Unstable atmosphere → Increase plume rise by 10–20%.
- Stable atmosphere → Decrease plume rise by about 20%.
Davidson and Bryant Equation
Another widely used plume rise equation is:
All symbols have the same meaning as in Holland's equation.
BIS (IS 8829 : 1978) Formulae for Plume Rise
The Bureau of Indian Standards (BIS) recommended the following equations:
(a) For Hot Effluent Releases
Applicable when heat release is approximately 10⁴ cal/s or more.
- QH = Heat release rate (cal/s)
- U = Wind speed (m/s)
(b) For Very Hot Releases Acting as Momentum Sources
- Vs = Stack gas velocity (m/s)
- D = Chimney diameter (m)
- U = Wind speed (m/s)
Factors Affecting Stack Height
- Emission rate of pollutants.
- Wind speed.
- Atmospheric stability.
- Temperature difference between flue gas and air.
- Stack diameter.
- Exit velocity of gases.
- Local topography.
Quick Revision
| Purpose | Equation |
|---|---|
| Particulate Matter | h = 74Q0.27 |
| SO₂ Emission | h = 14Qs0.3 |
| Effective Height | H = h + Δh |
| Hot Effluent (BIS) | Δh = 0.84(QH/U³)0.6 |
| Momentum Source | Δh = 3VsD/U |
Conclusion
The design of stack height is an important aspect of air pollution control engineering. Proper chimney height ensures adequate dispersion of pollutants and reduces their concentration near ground level. Various empirical equations are available for determining the required chimney height and plume rise based on pollutant emission rate, atmospheric conditions, and stack characteristics.
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