How do you calculate the volume in an oval shaped home heating oil fuel tank?

Answer 1

Hi,

Making the assumption that the tank consists of two oval-shaped end panels and has straight sides (the end view of the tank looks like an oval, the frontal view looks like a square), you must split the tank into neat, easily calculable 3-D geometric shapes and figure volume of each.

Let's say the tank is 5 feet high, 2 feet deep and 6 feet wide (the oval sides being 5x2).

You will need to "remove" the rounded top and bottom sections of the tank so that only a planar sided (cubic) shape remains. Calculate this volume, then to top and bottom sections (1/2 cylinders) and sum together.

The formula for the volume of a square-sided 3-D shape is Height times Depth times Width (HxDxW). The tank is two feet deep, so the ovals have a two foot diameter, and therefore a 1 foot radius. Removing the top and bottom half cylinder sections yields a center "cube" of 3 (5, minus 1, minus 1, for the top and bottom cylinders) x 2 x 6 = 36 cubic feet.

Now let's figure the volume of the two half cylinders and add those in. The formula for the volume of a cylinder is the area of the circular side times the length of the cylinder (in your case, the width of the tank). The area of a circle is "pi r squared" (sorry, no symbols on this keyboard). Pi is a constant at appox. 3.14. The radius of the cylinders base is half the diameter, or 1. The width of your tanks is 6 feet. So that's 3.14 x 1 x 6 = 18.84 cubic feet.

The total volume of this example is 54.84 cubic feet.

Of course you have a 1/2 cylinder on top and a 1/2 cylinder on the bottom of this tank, but the only way to do this calculation is to treat each as a whole cylinder and then divide by 2, to get a 1/2 cylinder. In your case, the top and bottom cylinders are identical, so these steps are unnecessary.