smigaldi said:
If the volume of a full cylinder is 1/2 * Pi * r2* l
why could I not take that result and then multiply it by the percentage of the level of the fluid as measured to the diameter of the cylinder?
Because the cylinder is laying on it's side, As you move up, the circular cross-section means that the increase in volume is not linear in respect to increase in height. Plus, once you pass the mid-point, the increase per inch of height is less each time...hence all the math...
For example, a 100" diameter cylinder of length 24", has a total volume of about 816 gallons. One can assume that 50% full (50% of Diameter), you would have 408 gals, and you'd be right. However, you cannot assume that at 25% diameter, you would have 204 gals...in fact, at 25"...you only have 159.5 Gals. 25% full is not met until just under 30". Grab a empty pop bottle and a tape measure
Try the attached spreadsheet. Just put in the Diameter and length, and it will work out the gallons at each inch measured. I made it up to 120 inches...easy enough to expand if you need. You can also just enter a number under 'Measured Height' and it will calculate gallons based on your diameter and Length.
But basically, this is what you want to put in an Excel cell...
=(length*((radius^2*(ACOS((radius-height)/radius)))-(SQRT(2*(radius*height)-height^2)*(radius-height))))/231
(assumes units are in inches, and you want it in gallons - thats the /231 at the end, and flat endcaps)