# Volume of a Cylindrical Tank

1. Sep 29, 2003

### Jeebus

I have to keep an inventory of how much is kept in a farm of tanks
outside my school. The tanks are cylindrical, which would be no
problem if they were standing on end, but they're not, they're lying
on their sides.

xx
x x
x----------x -Liquid level which is variable,
x x can go up or down
x x
x x
x x
xx

Imagine the above is a circle. I know the diameter of the circle,
and I can measure from the top of the circle down to the liquid level.
How can I use this information to derive the amount of liquid in the
circle? I hope to make a formula I can use in a spreadsheet.

Thanks so much.

2. Sep 29, 2003

### StephenPrivitera

The answer involves integral calculus. You can estimate the volume by estimating the area of the side of the cylinder and multiplying by the length. The answer I get is rather complicated. You have to solve the integral,
[inte]2lsqrt(r2-y2)dy taken from -r to h where r is the radius of the cylinder, h is the height of the water as measured from the bottom, and l is the length of the cylinder.

3. Sep 29, 2003

### Robert Zaleski

How are you gauging the tanks?
Gasoline stations have strapping tables prepared for their fuel tanks. These tables usually give volumes in 1/4" increments, which correspond to a dip stick measurement. If your using this method of measurement, you should check to see if any tables were developed for the tanks. You might want to contact a fuel tank manufacturer or maintenance outfit for guidance/suggestions, if no tables are available. Also, check to see if the tanks are set level.

4. Sep 29, 2003

### Robert Zaleski

Here's a way you can get a close estimate of the volume.

1. Take the diameter of a tank in feet and calculate the area of the circle.
2. Take this area and multiply it by the length of the tank.
This will give you the cubic feet of the tank.
3. Multiply the cubic feet by 7.48. This will give you the gallon capacity of the tank.
4. Draw a large circle to represent the end of the tank. Draw in the 'Y' axis and divide it into an equal number of parts to represent the foot marks of the circle; e.g.; if the diameter is six feet, divide the 'Y' axis into 6 equal parts. Now divide each of the 6 part into 12 equal parts.. These will represent the inch marks. Number these marks from bottom to top
5. Now you can start calculating the segments of the circle using the following formula;

........................R^2............pi x segment angle
Area of segment= ---- x -------------------------- - sin of segment angle
.........................2...............180 degrees

6. Take the area of the segment you just calculated and multiply it by the length of the tank times 7.48. Subtract this number from the total capacity of the tank you calculated previously. This will give you the remaining gallons in the tank.

7. Draw this segment on you circle. Note where the chord of the segment cuts the ‘Y’ axis. This point will be the gallons remaining for the height registered.

Happy calculating!

Last edited: Sep 29, 2003
5. Nov 29, 2003

### KiwiSam

The following formula will give the volume of the contents of a horizontal cylinder.

=0.5*ra*ra*(2*ACOS((ra-de)/ra)-SIN(2*ACOS((ra-de)/ra)))*le/1000000

Just paste this into a spreadsheet

"ra" is the radius of the cylinder
"de" is the depth of the contents (ie diameter minus measurement to surface)
"le" is the length of the cylinder