Nospill oil can mathematics
We've had several discussions of making nospill oil containers from cylindrical cans with a length of tubing inserted to provide access for an acid brush...
http://www.homemadetools.net/forum/s...-oil-can-53206
http://www.homemadetools.net/forum/spill-free-can-36967
Today I had occasion to derive the equations needed to set the geometry of such devices. Mathematically analyzing something like this may not be for everyone. Still, it's a nice example of how such analyses are done and may actually be useful for some.
The first sketch in the illustration shows the can in its normal, upright attitude. The key dimensions of the assembly are defined.
The second sketch shows the can lying on its side. In this attitude the oil height can only reach the bottom of the tube; any higher and it would leak out the tube. From this fact we can determine the volume of oil, V, that the can will be allowed to contain. Once V is known, we can use its value to determine how far into the can, L, the tube can project. The equations to the right of this sketch show how we use some simple geometry to determine V.
The minimum projection of the tube into the can, Lmin, is determined by requiring that the can not leak when it's turned upside down (see small sketch next to Lmin equation.
The maximum projection, Lmax, is found from the topmost sketch. The tube has to just touch the surface of the oil when the can is filled with a volume, V, of oil that won't spill out when the can is lying on its side.
