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Numerical Problem 1 
• Coal with calorific value of 32 MJ/kg is burnt 
at a rate of 1.25 kg/sec. If the sulfur content in 
the coal is 1.5%. What is the rate of emission 
of SO2 in Tpd/MW. Assume that 3 units of 
heat energy is converted into 1 unit of 
electrical energy. Sulfur content in the ash may 
be assumed to be 8%.
Solution 
Heat input to the plant is = = 
Elecrical Capacity of the power plant is =40/3=13.3 MW 
Sulfur burnt = = 
Sulfur in the emission = 0.01875×0.92 = 0.01725 
We know: 
S + O2 SO2 
SO2 Emission = = = 
Rate of emission of SO2 Tpd/MW = = 0.22 Tpd/MW
Numerical Problem 2 
• In your township, you want the automobiles to 
be tuned up for limiting the air-pollution. Find 
out the optimum air-to-fuel ratio (by mass) for 
a car which uses Diesel with chemical formula 
C14H30.
Solution 
C14H30 + 21.5 O2 = 14 CO2 + 15H2O 
Assuming, air contains 21% O2 and 79% N2 by volume. 
= 
(mass ratio)
Numerical Problem 3 
• In the township, a coal-fired power plant 
which will use high-sulfur coal which 
produces flue gas containing SO2 at a 
concentration of 0.07 ppm. Ambient air 
temperature is 298 K. The Indian air quality 
standard for the emission of SO2 from industry 
is 80 μg/m3. Determine whether the emission 
from the power plant shall be within the 
permissible limit.
Solution 
SO2 → 32 + 2×16 = 64 
SO2 concentration in μg/m3 (air) = 0.07 ppm × 64 × 
P = 1 atm 
T = 298 K 
SO2 Conc. = 0.07 × 64 × = 183.2 μg/m3 
Emission from the power plant in not within permissible limit.
Numerical Problem 4 
• The power plant in the township shall be of 100 MW 
capacity. It converts one-third of the heat energy to 
electrical energy. The rest of the heat energy appears 
as waste heat. Flue gas takes away 20% of waste heat 
and the rest of the waste heat is taken away by the 
cooling water which is supplied from the river. The 
pollution control authority restricts the rise of cooling 
water temperature to 10 oC from its baseline value of 
25 oC. River flows at a rate of 50 m3/s. What should be 
the minimum flow rate of cooling water used in the 
plant? Take the specific heat capacity of water to be 
equal to 4l80 J/(kg.oC).
Solution 
STEP-1: 
Total heat input to the plant = 300 MW 
Waste heat = (2/3) × 300 MW = 200 MW 
Cooling water takes out 80% of the waste heat. 
Heat input into the cooling water 
= 200 MW × (80/100)= 160 MW
Solution 
STEP-2: Water Input = 
= 3.8 
= 13780
Numerical Problem 5 
A power plant of 200 MW capacity is using imported coal having 
heating value of 28.85 MJ/kg. The sulphur and mercury content of 
the coal is 2.46% and 23.12 μg/kg respectively. Determine the 
amount of SO2 and mercury emitted in air by this plant annually 
assuming that 5.85% sulphur and 2.53% mercury remain in the 
ash. The conversion efficiency of the plant is 38.51% and the plant 
runs for 300 days in a year. 
Numerical Problem 6 
A new coal fired power plant has been built using sulphur emission 
control system that is 70.5% efficient. If all of the sulphur oxidizes 
to SO2 and the emissions of SO2 are limited to 0.3 kg per million 
BTU of heat into the power plant, what maximum percent sulphur 
content can the fuel have? 1 BTU=1055 J. 
(a) If 33.33 MJ/kg coal is burnt ? 
(b) If 19.80 MJ/kg coal is burnt ?
Numerical Problem 7 
A police man is on duty at a traffic intersection where the CO 
concentration is 45 ppm. Calculate the % COHb of the police man 
if he remains on duty for 2 hours continuously. 
Numerical Problem 8 
The OSHA (Occupational Safety and Health Administration) 
standard for worker exposure to 8 hour of CO is 50 ppm. What 
percentage of COHb would result from this exposure? 
Numerical Problem 9 
Convert the following air quality standards established by the CPCB, 
New Delhi from ppm to mg/m3 at 25 oC and 1 atm or vice verca. 
a.CO2=5000 ppm 
b.Formaldehyde (HCHO)=3.6 mg/m3 
c.Nitric oxide(NO)=25 ppm
Numerical Problem 9 
Calculate 1 ppm SO2 concentration in microgram/m3 at 0oC & 1.2 
atm pressure. 
Numerical Problem 10 
Volumetric flow rate of flue gas coming out of a 500 MW coal power plant 
is 2.5 m3/s. To meet the national emission standards, it is estimated that 
98.5% of the total particulate matter is required to be removed by 
electrostatic precipitator. Calculate the total area of the collection plates 
of the electrostatic precipitator if the average drift velocity of the particles 
is 0.12 m/s. 
Numerical Problem 11 
A droplet of water is of 2.5 micron size. Determine its settling velocity in 
air at ambient temperature and pressure conditions. The viscosity of air 
may be taken as 0.01725 g/m s.
Numerical Problem 12 
It has been reported that wind velocity at 10 height is 2.6 m/s. Calculate the wind 
velocity at the top of a building where an TV antenna has been fixed at a height of 
150 m from the ground. The p=0.4 value may be taken corresponding to the stability 
class on that day. 
Numerical Problem 13 
A power plant has a 100 m stack with inside radius of 1 m at top. The flue gases 
leave the stack with an exit velocity of 10 m/s at a temperature of 120 oC. Ambient 
temperature is 16 oC, winds at the stack height are estimated to be 5 m/s and 
surface wind speed is 3 m/s and it is a cloudy summer day in Vancouver. 
Determine the effective stack height of this stack. 
Numerical Problem 14 
A coal power plant in a rural area is emitting 100 g/s of SO2 in the month of June 
2010 when the incoming solar radiation is strong. Do you think that the villagers of 
a nearby area are exposed to SO2 concentration higher than the national air 
quality standard permits? The village is approximately 1.0 km downwind and 0.2 
km off the centreline from the power plant. The wind speed at the surface (at 10 
m) is 1.5 m/s and the terrain is plain in nature. The effective stack of the power 
plant is of 140 m. The 24-hour average national air quality standard for rural area 
is 80 μg/m3. (Assume P = 0.07, Sy = 210 m, and Sz = 450 m for the given 
conditions and coordinates).
Problem 1 
An Indian city is generating solid waste @ 1.2 
kg/day per capita for four months and @ 0.5 
kg per day per capita for eight months in a 
year. The population of the city is 2.489 
million as per the census of 2011. It is planned 
to earmark land for land filling of the garbage 
for a period of five years. Assuming the 
landfill garbage density of 452 kg/m3 and a 
10.5 m lift determine the area for (a) 25% soil 
in cell volume (b) 30% soil in cell volume.
Problem 2 
Estimate the landfill area needed to 
handle 10 year’s Municipal Solid Waste 
for a town of 250,000 people. Assume 
per capita solid waste generation is 0.5 
kg/day and landfill density of 600 kg/m³, 
and a single 3m lift. Assume that 20 
percent of the cell volume is soil used for 
cover.
Problem 3 
A landfill site is producing 3500 Nm3 
biogas daily. H2S content of biogas is 
0.87%. Determine the SO2 emission if this 
gas is used in I.C. engines for the 
generation of electricity. Also determine 
the electricity generation capacity. The 
heating value of biogas is 18.58 MJ/Nm3 
and only 38.5% of the thermal energy is 
converted into electricity by IC engine 
coupled alternators.

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Ce 105 12 air pollution - numerical problems

  • 1. Numerical Problem 1 • Coal with calorific value of 32 MJ/kg is burnt at a rate of 1.25 kg/sec. If the sulfur content in the coal is 1.5%. What is the rate of emission of SO2 in Tpd/MW. Assume that 3 units of heat energy is converted into 1 unit of electrical energy. Sulfur content in the ash may be assumed to be 8%.
  • 2. Solution Heat input to the plant is = = Elecrical Capacity of the power plant is =40/3=13.3 MW Sulfur burnt = = Sulfur in the emission = 0.01875×0.92 = 0.01725 We know: S + O2 SO2 SO2 Emission = = = Rate of emission of SO2 Tpd/MW = = 0.22 Tpd/MW
  • 3. Numerical Problem 2 • In your township, you want the automobiles to be tuned up for limiting the air-pollution. Find out the optimum air-to-fuel ratio (by mass) for a car which uses Diesel with chemical formula C14H30.
  • 4. Solution C14H30 + 21.5 O2 = 14 CO2 + 15H2O Assuming, air contains 21% O2 and 79% N2 by volume. = (mass ratio)
  • 5. Numerical Problem 3 • In the township, a coal-fired power plant which will use high-sulfur coal which produces flue gas containing SO2 at a concentration of 0.07 ppm. Ambient air temperature is 298 K. The Indian air quality standard for the emission of SO2 from industry is 80 μg/m3. Determine whether the emission from the power plant shall be within the permissible limit.
  • 6. Solution SO2 → 32 + 2×16 = 64 SO2 concentration in μg/m3 (air) = 0.07 ppm × 64 × P = 1 atm T = 298 K SO2 Conc. = 0.07 × 64 × = 183.2 μg/m3 Emission from the power plant in not within permissible limit.
  • 7. Numerical Problem 4 • The power plant in the township shall be of 100 MW capacity. It converts one-third of the heat energy to electrical energy. The rest of the heat energy appears as waste heat. Flue gas takes away 20% of waste heat and the rest of the waste heat is taken away by the cooling water which is supplied from the river. The pollution control authority restricts the rise of cooling water temperature to 10 oC from its baseline value of 25 oC. River flows at a rate of 50 m3/s. What should be the minimum flow rate of cooling water used in the plant? Take the specific heat capacity of water to be equal to 4l80 J/(kg.oC).
  • 8. Solution STEP-1: Total heat input to the plant = 300 MW Waste heat = (2/3) × 300 MW = 200 MW Cooling water takes out 80% of the waste heat. Heat input into the cooling water = 200 MW × (80/100)= 160 MW
  • 9. Solution STEP-2: Water Input = = 3.8 = 13780
  • 10. Numerical Problem 5 A power plant of 200 MW capacity is using imported coal having heating value of 28.85 MJ/kg. The sulphur and mercury content of the coal is 2.46% and 23.12 μg/kg respectively. Determine the amount of SO2 and mercury emitted in air by this plant annually assuming that 5.85% sulphur and 2.53% mercury remain in the ash. The conversion efficiency of the plant is 38.51% and the plant runs for 300 days in a year. Numerical Problem 6 A new coal fired power plant has been built using sulphur emission control system that is 70.5% efficient. If all of the sulphur oxidizes to SO2 and the emissions of SO2 are limited to 0.3 kg per million BTU of heat into the power plant, what maximum percent sulphur content can the fuel have? 1 BTU=1055 J. (a) If 33.33 MJ/kg coal is burnt ? (b) If 19.80 MJ/kg coal is burnt ?
  • 11. Numerical Problem 7 A police man is on duty at a traffic intersection where the CO concentration is 45 ppm. Calculate the % COHb of the police man if he remains on duty for 2 hours continuously. Numerical Problem 8 The OSHA (Occupational Safety and Health Administration) standard for worker exposure to 8 hour of CO is 50 ppm. What percentage of COHb would result from this exposure? Numerical Problem 9 Convert the following air quality standards established by the CPCB, New Delhi from ppm to mg/m3 at 25 oC and 1 atm or vice verca. a.CO2=5000 ppm b.Formaldehyde (HCHO)=3.6 mg/m3 c.Nitric oxide(NO)=25 ppm
  • 12. Numerical Problem 9 Calculate 1 ppm SO2 concentration in microgram/m3 at 0oC & 1.2 atm pressure. Numerical Problem 10 Volumetric flow rate of flue gas coming out of a 500 MW coal power plant is 2.5 m3/s. To meet the national emission standards, it is estimated that 98.5% of the total particulate matter is required to be removed by electrostatic precipitator. Calculate the total area of the collection plates of the electrostatic precipitator if the average drift velocity of the particles is 0.12 m/s. Numerical Problem 11 A droplet of water is of 2.5 micron size. Determine its settling velocity in air at ambient temperature and pressure conditions. The viscosity of air may be taken as 0.01725 g/m s.
  • 13. Numerical Problem 12 It has been reported that wind velocity at 10 height is 2.6 m/s. Calculate the wind velocity at the top of a building where an TV antenna has been fixed at a height of 150 m from the ground. The p=0.4 value may be taken corresponding to the stability class on that day. Numerical Problem 13 A power plant has a 100 m stack with inside radius of 1 m at top. The flue gases leave the stack with an exit velocity of 10 m/s at a temperature of 120 oC. Ambient temperature is 16 oC, winds at the stack height are estimated to be 5 m/s and surface wind speed is 3 m/s and it is a cloudy summer day in Vancouver. Determine the effective stack height of this stack. Numerical Problem 14 A coal power plant in a rural area is emitting 100 g/s of SO2 in the month of June 2010 when the incoming solar radiation is strong. Do you think that the villagers of a nearby area are exposed to SO2 concentration higher than the national air quality standard permits? The village is approximately 1.0 km downwind and 0.2 km off the centreline from the power plant. The wind speed at the surface (at 10 m) is 1.5 m/s and the terrain is plain in nature. The effective stack of the power plant is of 140 m. The 24-hour average national air quality standard for rural area is 80 μg/m3. (Assume P = 0.07, Sy = 210 m, and Sz = 450 m for the given conditions and coordinates).
  • 14. Problem 1 An Indian city is generating solid waste @ 1.2 kg/day per capita for four months and @ 0.5 kg per day per capita for eight months in a year. The population of the city is 2.489 million as per the census of 2011. It is planned to earmark land for land filling of the garbage for a period of five years. Assuming the landfill garbage density of 452 kg/m3 and a 10.5 m lift determine the area for (a) 25% soil in cell volume (b) 30% soil in cell volume.
  • 15. Problem 2 Estimate the landfill area needed to handle 10 year’s Municipal Solid Waste for a town of 250,000 people. Assume per capita solid waste generation is 0.5 kg/day and landfill density of 600 kg/m³, and a single 3m lift. Assume that 20 percent of the cell volume is soil used for cover.
  • 16. Problem 3 A landfill site is producing 3500 Nm3 biogas daily. H2S content of biogas is 0.87%. Determine the SO2 emission if this gas is used in I.C. engines for the generation of electricity. Also determine the electricity generation capacity. The heating value of biogas is 18.58 MJ/Nm3 and only 38.5% of the thermal energy is converted into electricity by IC engine coupled alternators.