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| Math Central | Quandaries & Queries |
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Question from Kinsley: Hello, I have a fuel tank with a broken gage. It is a 2000 gallon tank. THe dimensions are 64" dia. x 146" long. The fuel gage doesn't work, so the only measurement I can do is put a stick in it to see what is left. Currently it is at 19". PLEASE NOTE: the tank is laying on its side, meaning the long side is on the ground. So, how do I determine how much fuel is in the tank by the inches remaining? Thank you very much. |
Hello Kinsley,
Determining the level precisely requires some knowledge of Calculus. Also, a couple assumptions are “built in” to the formula below:
- The tank is perfectly level, and
- The dipstick is perfectly plumb.
If we assume these conditions hold, then a (very good approximate) formula is given by:
Where h is how many inches of fuel on the dipstick, and V is volume in U.S. gallons.
This formula is quite SCARY, and probably far more precise than necessary.
I recommend keeping a chart with the tank based on some handy divisions of the dipstick, such as this one:
Dipstick Height (in.) |
1 |
2 |
3 |
4 |
5 |
6 |
Etc.... |
Volume (US gal.) |
6.7 |
18.9 |
34.5 |
52.9 |
73.6 |
96.2 |
Etc.... |
If you require better approximations divide these into smaller intervals, say of a half inch or perhaps quarter inch.
With such a large tank, small differences on the dipstick can make quite a difference when it comes to volume.
Write back if you need some clarification, or if you are interested in how the formula was obtained.
Tyler
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