   SEARCH HOME Math Central Quandaries & Queries  Question from Phillip: Hello, my question is: If I spilled 25 gallons of diesel fuel on a flat surface how much area would the spill cover? How would I mathematically figure it out? Thanks! Phillip,

I did some Internet searching to attempt to determine the thickness the fuel would attain if allowed to spread on the surface of water. This will depend on many factors but a figure I found in a few places is 1 millimeter. Here is one reference. To get an more accurate determination you will need to contact someone with knowledge of the behaviour of oil on a flat surface.

I am going to assume a 1 mm thickness. I then asked Google how many cubic millimeters are is 25 gallons (I typed 25 gallons in cubic millimeters into the Google search engine) and obtained 25 US gallons = 94 635 294.6 cubic millimeters. I then divided by the thickness to obtain the surface area. Since the assumed thickness is 1 millimeter this gave me 94 635 294.6 square millimeters. This time I typed 94635294.6 square millimeters in square feet into Google and obtained 94 635 294.6 (square millimeters) = 1 018.64583 square feet.

I hope this helps,
Harley

Phillip,

That's a physics question, not a math question! Factors that would affect the answer are porosity, slope, whether the surface attracts or repels nonpolar nonionic fluids such as diesel, and surface roughness (at an appropriate scale that depends on other factors).

For very porous surfaces (deep gravel) the answer might be a few square inches - on the top. If we assume a nonabsorbing, nonporous medium, I would guess that the answer could range from a few tens of square meters for a very rough surface (for which surface tension would trap significant quantities of fluid in dents and cracks on the millimeter scale) to square kilometers or more (as a film on water).

Professionals in fuel delivery or environmental cleanup could probably give you a fairly good answer based on experience. Try the Yellow Pages. And please don't experiment <grin>.

Good hunting!
-RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.