Saturday, May 1, 2010

BP Oil Spill

An offshore oil rig off the coast of Louisiana burned and sank in late April 2010, causing a massive leak of crude oil into the gulf of Mexico. The New York Times reported on it here, and you can watch a video clip of a news report on the spill here:

Mathematics Problems:
We can make some interesting mathematics problems by taking some information from the actual situation and making some simplifying assumptions to make the problems solvable on a reasonable amount of time

  • The well is leaking 5,000 barrels of oil per day (Thought to be true initially, but later raised a great deal)
  • The well is located about 5 miles from the coast (True)
  • The oil will form a circle as it reaches the surface of the water. (Not True)
  • The oil slick will have a consistent thickness of 100 µm (micrometres) (Not True)

  1. Please find the radius of the spill after 1 day,2 days,3 days,4 days,5 days,10 days, and 20 days. (Do each calculation by first finding the volume of the oil released, then finding the radius of the cylinder 100µm thick that contains that much oil.

  2. Find an explicit equation that gives the radius of the oil slick as a function of time.

  3. Please graph the radius of the spill as a function of time.

  4. Please estimate how long it will take the spill to reach the coast.

  5. Write a clear explanation of why the volume of the oil and the radius of the slick are not directly proportional.


  1. Has anyone produced the graph in #3 yet?

  2. Yes...most of my students are able to build a function of this type and graph it. The two big weaknesses this problem brought out for many of my students were:

    1) keeping track of the different units and changing to ocnsistent units, and

    2) the concept that radius and volume are not directly proportional. Students have a knee jerk reaction to want to say that once they find the radius after 1 day, the radius for 5 days will be five times the first answer. In this way the problem is a great precursor to the related rates problems that will arise in calculus.