CE 397: Environmental Risk Assessment

Homework Assignment #4: Atmospheric Transport Modeling and Indoor Air Quality

Spring, 1998




  1. A process vent (stack) emits a hot gas containing benzene. The following conditions can be assumed for the stack, gas stream and environment.


Benzene concentration is stack gas = 2 parts per thousand by volume

Stack gas temperature = 130 C

Physical stack height = 25 m

Stack diameter = 1 m

Stack gas exit velocity = 8 m/s

Wind speed at 10 m above surface = 3 m/s

Wind speed at physical stack height = 4 m/s

Temperature at ground-level = 8 C

Environmental lapse rate = -1 C/km

Rural setting


  1. Determine and plot the ground-level centerline concentration of benzene as a function of downwind distance. Your plot should extend to a distance to which the benzene concentration is significantly lower than (say 25% of) the maximum concentration that you pass through.

  3. Repeat part (a) assuming an environmental lapse rate of 12 C/km on a sunny summer day in which the ground-level temperature is 30 C and all other parameters are the same as listed above. Compare your results with those obtained in part (a).



  1. For each of the two conditions listed in problem 1, estimate the maximum ground-level concentration of benzene and distance to the maximum using the nomogram provided in lecture. Compare your results to the maximum concentrations determined in problem 1.


  3. A line source is oriented parallel to the mean wind and emits particulate matter at a uniform rate of 100 mg/m-s in a rural setting. The closest human receptor (a deranged, retired university professor named Leo who spends all of his time on his front porch lecturing to a hypothetical audience of enthusiastic students) lives 100 m downwind from the closest edge of the source. The source itself is 150 m in length (see figure below). Determine the concentration (in micrograms per cubic meter) at Leo's front porch given a ground-level wind speed of 1 m/s and a wind speed of 4 m/s at 10 m on a clear night. You may assume that the line source is located at ground-level and that there is no plume rise.


  5. Leo (the guy from problem 3) uses well water that is chemically challenged with benzene. The concentration of benzene in the water supply is 2 mg/L!


Assume that Leo spends 20 minutes showering every day (while in the shower he continues to lecture to a group of hypothetical, enthusiastic, but shocked students). You may assume the following conditions for your analysis:


Volume of Leo's shower stall = 1.8 m3.

Leo likes a high flow rate of water: 9.1 L/min.

Leo likes a coarse water spray: KLA = 1.7 L/min

Leo likes his showers fairly warm: water temperature = 35 C

Air flow rate entering and exiting Leo's shower stall = 379 L/min

Initial benzene concentration in Leo's shower (start of showering event) = 0 mg/L

Concentration of benzene entering Leo's shower from atmosphere outside of shower = 0 mg/L

Leo breathes at a rate of 20 m3/day

Leo drinks 2 L of water per day


Compare the amount of benzene that Leo inhales on a daily basis (while showering only) to that which he ingests on a daily basis.