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ME 106 Fluid Mechanics

Modeling air pollution
The sketch in Fig. 1 gives you the parameters you need for the problem. The downtown of Houston is approximated to be 5 km long and 5 km wide. Incoming air is assumed clean, and the emission rate of ozone is given per m2 of city surface area from cars. The top boundary can be assumed to have zero pollutant flux. Assuming these conditions have been prevalent for a long time, and assuming in the box model of the city, pollutants in the atmosphere are well mixed.
(a) What is the concentration of ozone in the city air as a function of wind speed U?

(b) The EPA standards for ozone are about 0.15 mg/m3, at what wind speed U will these standards be exceeded?

(c) Now we are going to develop a simplified version of a numerical air quality model. Instead of putting one box over the city, model the air above it as 3 boxes in the mean wind direction (each box is 5/3 km long and 5 km wide). Each box is also assumed well mixed, but now you can solve the problem for box 1, then assume its C out is the C in for box 2, then do the same for boxes 2 and 3. For U =1 m/s, what are the concentrations in boxes 1, 2, 3 and are the standards exceeded anywhere?
                                                                            numerical air quality model

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