How many gallons of fluid are in a large cylinder fuel tank that is 13 feet in diameter and 28 feet long and laid horizontally filled to 3.5 feet?

Answer 1

You have to find the area of end of the tank occupied by the fluid. First, the area of one end of the tank is

3.14159 x (13/2)^2 = 132.7 ft^2

If you draw two lines, on one end of the tank, from the center of the tank to the intersection of top of the fluid at the circumference of the tank, the length of each line is equal to the radius of the tank (6.5'). A perpendicular line drawn from the center to the fluid level line, is the tank radius - fluid depth = 6.5' - 3.5' = 3.0'. The angle between the vertical line and one of radius lines to the edge of the liquid, is

ACOS(3.0 / 6.5) = 62.51 deg.

The angle between both of the first two lines drawn to each edge of the liquid is 2 x 62.51 deg = 125.03 deg. The area of this section that looks like a piece of pie, is

132.7 ft^2 x 125.03 / 360 = 46.1 ft^2.

1/2 of the length of the top of fluid line on the end of the tank is

square-root(6.5^2 - 3.0^2) = 5.77 ft

Of the pie-shaped piece, the area of the triangular portion that is not wetted by fluid is

3.0' x 5.77' = 17.3 ft^2.

The area of the wetted end of the tank therefore is the pie-shaped area minus the non-wetted trianglular area =

46.1 ft^2 - 17.3 ft^2 = 28.8 ft^2.

The volume of the fluid is the area of the wetted end x length =

28.8 ft^2 x 28 ft = 806.1 ft^3.

Since there are 7.48 gal / ft^3, total volume in gallons =

806.1 ft^3 x 7.48 gal/ft^3 = 6,029 gal