Modeling Air Quality

Your residence is located one mile downwind and in a direct line from the two forbidding smoke stacks in the above photograph. Surely you will have some concentration of pollutants in the vicinity of your home. Now imagine the situation where everything is the same but the wind is blowing twice as hard. Do you think you will get a higher concentration of pollutants at your home or a lower concentration?

Observe the smoke plumes emitted from the two smoke stacks in the above photograph. Are the gasses emitted from these smoke stacks likely to be very hot?

In the above picture the sky seems overcast. Is the concentration of air pollution at your home likely to increase or decrease if the sun were to shine brightly and the clouds disperse?

The answers to these questions and many others are all taken into account in a mathematical model of air pollution calledThe Gaussian Plume Model. The Gaussian Plume Model provides a formula for the calculation of concentration of pollutants at any location downwind from the source of emission and at any given time after the emission started.

The Gaussian Plume Model

The table and graphs below represent typical concentration calculations and graphing for a simplified case of the plume model, the case of one dimensional diffusion. Both calculations and graphs were carried out with Microsoft Excel spreadsheet program.

 M = 100 lb D=.025 lb^2/min 1 10 20 30 40 50 -2 7.58E-16 1.033611 5.400466 8.588459 10.38032 11.34004 -1.5 3.02E-08 5.948022 12.95504 15.39053 16.07735 16.09228 -1 0.008102 20.76064 24.20321 23.34585 21.97514 20.6629 -0.5 14.6487 43.95027 35.21546 29.97667 26.50707 24.00686 0 178.4577 56.43326 39.90434 32.58176 28.21663 25.23772 0.5 14.6487 43.95027 35.21546 29.97667 26.50707 24.00686 1 0.008102 20.76064 24.20321 23.34585 21.97514 20.6629 1.5 3.02E-08 5.948022 12.95504 15.39053 16.07735 16.09228 2 7.58E-16 1.033611 5.400466 8.588459 10.38032 11.34004

Back to Math 108V Poster's Main Page