**The Best of Creative Computing Volume 1 (published 1976)**

The next task is to "patch up" the model given by (1) to make it more realistic. First, we will redefine P. Let P stand for the total number of grams of pollutants of any kind in the system. To account for wind effects, assume that if W is the wind velocity in miles per hour during any hour-long period, that (W/50)P is the amount of pollutants that is removed during that hour. We will limit wind velocities to the range 0 to 50 mph. As you can see, a velocity of 0 means that no pollutants are removed during the hour, and a velocity of 50 mph implies that all the smog is blown out during the hour. Do you think this is reasonable? If not, you might want to make assumptions of your own. Finally, let's assume that R2 P of the pollutants disappear during an hour from dissipation mechanisms. Now we can write down our new model: Pnew=Pold+R1N-W/50Pold-R2Pold. (2) P (either "old" or "new") stands for the total number of grams of pollutants in the system. R1 is the total amount of pollutants (in grams) produced per hour per car. N is the number of cars operating (remember that we are assuming 40 mph). W is the wind velocity in miles per hour. R2 is the decimal part of the pollutants that is dissipated each hour from causes other than wind or weather. If we let C stand for the concentration of pollutants in milligrams (thousandths of a gram) per cubic foot, then C must be given by C = 1000Pnew/V (3) where V is the volume of the system in cubic feet. The combination of Equations (2) and (3) gives us our new model and allows us to compute the pollutant concentration in milligrams per cubic foot. EXERCISE 8 - A New Model Suppose we examine an intersection of two major freeways. Let is assume that each freeway has four lanes of traffic in each direction, Consider as our 'system " a block of air, 2000 feet on a side and 500 feet high, centered on the freeway intersection. Assume that the traffic flow saturates the freeways and remains constant. Assume a wind velocity of 5 mph, and R2 = .01. Write a BASIC program using Equations (2) and (3) to print out C every hour, assuming that the initial value of P is zero. Run the program until C does not change further. Draw a rough graph of your results. EXERCISE 9 - Equilibrium Concentration If C does not change, the system has reached equilibrium. When this is true, Pnew = Pold = Peq . Use some simple algebra in Equations (2) and (3) to predict mathematically the equilibrium value of C. Check your answer against the results of Exercise 8. EXERCISE 10 - Turning the Wind Off Use the program from Exercise 8 to investigate the effects of turning the wind on and off. Your program printouts should show two equilibrium values of concentration, with and without wind! Can you find both of these algebraically? 226