Suppose that Fairbanks Alaska can be treated as a box with dimensions of 9.2 km by...

  

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Suppose that Fairbanks Alaska can be treated as a box with dimensions of 9.2 km by 9.2 km and a height of 100 m. Sources in the town for PM2.5 include cars, trucks, and wood stoves and these emit 100 kg/hr of PM 2.5 into the airshed. Wind blows through the town at a steady 4 m/s. Assume that the pollution in this box model airshed is perfectly mixed and the ambient conditions outside of the city are negligible for PM 2.5. Also assume that the PM 2.5 has a first order decay constant of 0.48 hr. (a) (10 pts) What is the steady-state concentration of PM2.5 (g/m) in the airshed? Be sure to include a labeled drawing, the general mass balance equation based on your drawing, an explanation of which terms can be canceled, a derived expression for the steady-state concentration, and your answer in g/m. (b) (10 pts) Assume that the inversion layer lifts increasing the height of the box to 200 m and the windspeed increases to 5 m/s. This shift in wind also brings in some air that has pollution from a power plant upwind of the city. The ambient air concentration coming into the city from this power plant is 8 ug/m. All other variables are the same as in part (a). How will this modify the steady state concentration of PM2.5 in the city? Include all the parts of a box model calculation that are listed in italics in part (a). Assume that the decay rate stays the same. (c) (5 pts) If the wind stops and the sources are turned off in both (a) and (b), how will the time it takes to decrease the concentration to half of the values you calculated compare between the two? Assume the first order decay rate stays the same for both (K = 0.48 hr). If you don't have values for (a) and (b) explain how the time to reach 1/2 of your steady state concentration changes between a city with 20 g/m vs. one with 5 g/m of PM2.5 at steady state. A correct answer here can be qualitative only. Suppose that Fairbanks Alaska can be treated as a box with dimensions of 9.2 km by 9.2 km and a height of 100 m. Sources in the town for PM2.5 include cars, trucks, and wood stoves and these emit 100 kg/hr of PM 2.5 into the airshed. Wind blows through the town at a steady 4 m/s. Assume that the pollution in this box model airshed is perfectly mixed and the ambient conditions outside of the city are negligible for PM 2.5. Also assume that the PM 2.5 has a first order decay constant of 0.48 hr. (a) (10 pts) What is the steady-state concentration of PM2.5 (g/m) in the airshed? Be sure to include a labeled drawing, the general mass balance equation based on your drawing, an explanation of which terms can be canceled, a derived expression for the steady-state concentration, and your answer in g/m. (b) (10 pts) Assume that the inversion layer lifts increasing the height of the box to 200 m and the windspeed increases to 5 m/s. This shift in wind also brings in some air that has pollution from a power plant upwind of the city. The ambient air concentration coming into the city from this power plant is 8 ug/m. All other variables are the same as in part (a). How will this modify the steady state concentration of PM2.5 in the city? Include all the parts of a box model calculation that are listed in italics in part (a). Assume that the decay rate stays the same. (c) (5 pts) If the wind stops and the sources are turned off in both (a) and (b), how will the time it takes to decrease the concentration to half of the values you calculated compare between the two? Assume the first order decay rate stays the same for both (K = 0.48 hr). If you don't have values for (a) and (b) explain how the time to reach 1/2 of your steady state concentration changes between a city with 20 g/m vs. one with 5 g/m of PM2.5 at steady state. A correct answer here can be qualitative only.