June 2017

This problem is closed. The September version is coming soon.

Inclined to Tank You

One end of a fuel tank stand has settled causing the tank to be sloped at 10°00’ from back to front. This prevents some fuel from draining out of the bung at the bottom of the tank’s front.tank1

The tank is cylindrical with a 48” diameter and 72” length (inside dimensions). The bung is 2-1/2” diameter and its opening is located 1” above the inside tank bottom.

tank3     tank2
How much fuel, to nearest 0.01 gallon, is left in the tank? Assume 10% ethanol fuel with 89 octane rating (R+M method), tank wall roughness is 0.00015 ft, and meniscus effect is negligible.

 

S D B Total Name      Date      Comments
6 10 4 20 Larry Schmit 20 Jun Used calculus & MathCAD to correctly solve the problem.
4 8 5 17 Norm Hanson 25 Jun Applied average end area formula (AEAF) but made a math error. AEAF assumes linear relationship while the tank surface is curved.
4 6 2 12 Scott Dischler 26 Jun Also used AEAF. Even in linear situations, AEAF over-estimates volume.Scott's solution was about 15% high.
6 4 4 14 Al Melbard 02 Jul Applied hybrid AEAF by cutting the entire volume into slices and computing their individual volumes. 1" slices were small enough to hit the correct voulme to the resolution specified. See Al's explanation and spreadsheet.

updated 27 Aug 2017

logo

fb