How Much Oil's Spilling? It's Not Rocket Science

May 23, 2010 — -- How much oil has leaked into the Gulf of Mexico? Many, including BP, have made estimates and remarked on the difficulty of determining the answer.

As Steve Wereley, an engineering professor at Purdue University, has shown, however, and as many others would have shown had pictures of the leak been released earlier, an approximate estimate is quite easy to come by and indicates a vastly greater oil spill than BP has admitted.

Wereley and a few other scientists, who have come to the same general conclusions, have performed a public service.

Basically, the method for determining oil spillage boils down to common sense and high school (or even middle school) geometry, specifically the formula for the volume of a cylinder.

Let's first assume that the oil is spilling out through the pipe and maintaining its cylindrical shape. It's not of, of course. The oil is an ever-moving, shapeless blob, but the volume of this blob of oil is the same as the volume of a long cylinder of oil extending out of the pipe, and this latter volume is much easier to calculate.

So what is the ever-growing volume of this cylinder? Geometry tells us the volume of a cylinder is the circular cross-sectional area of the cylinder (BP certainly knows this because it knows the radius of the pipe is 10.5 inches) multiplied by the height (or because it's horizontal here, the length), h.

And what is its height (or length), h? Again elementary math comes to the rescue.

The length of the imagined lengthening cylinder of oil equals the rate of flow of the oil multiplied by the time it's been flowing. That is, h = v*t.

We certainly know the time. The break occurred on April 20.

The calculation is then simply a matter of plugging the right values into the formula for the volume of a cylinder: V=pi*r^2*v*t, where, once again, V is the volume of a cylinder, t is the time the oil has been leaking, and v is the flow rate of the oil through the cylinder.

The flow rate is not known exactly, so what Wereley did was to turn the poor video snippet (Wereley suggested that BP released what they thought was the least helpful clip) into a series of still pictures. Then he calculated the velocity of particles in the flow by employing software that analyzed the still pictures frame by frame and pixel by pixel to come up with an estimated flow rate for the oil of 2 feet per second.