Problem

The Los Angeles basin floor covers approximately 700 square miles $(2*10^{10} ft^2)$ and is almost completely surrounded by mountain ranges. If one assumes inversion height in the basin of $2000$ feet, the corresponding volume of air in the basin is $4*10^{13} ft^3$. Using this system volume we can model the accumulation and depletion of air pollutants. As a very rough first approximation, we shall treat the Los Angeles basin as a well-mixed container (similar to a CSTR) in which there are no spatial variations in pollutant concentrations. We will also simplify the system by considering only the pollutant carbon monoxide and assuming that its only source is from automobile exhaust. On the average we will further suppose that there are 400,000 cars operating in the basin at any one time. Each car gives off approximately 3000 standard cubic feet of exhaust each hour containing $2\%$ mol carbon monoxide.

We shall perform an unsteady-state mole balance on CO as it is depleted from the basin area by a Santa Ana wind. Santa Ana winds are high-velocity winds that originate in the Mojave Desert just to the northeast of Los Angeles. This clean desert air flows into the basin through a corridor assumed to be $20$ miles wide and $2000$ ft high (inversion height) replacing the polluted air, which flows out to sea or toward the south. The concentration of CO in the Santa Ana wind entering the basin is $0.08$ ppm $(2.04*10^{-10} \frac{lb*mol}{ft^3})$.