Tim,

First of all, if your measurements are exact (40 feet long, 12 feet in diameter), the volume of your tank is a bit less than 40,000 gallons:

V = 40 * 36 * Pi = 4524 cubic feet = 33840 gallons.

Below is the folmula to calculate the amount of water in your tank. Not an easy one. :)

Let H is the level of water from the bottom that you have measured. The volume of water in the tank in cubic feet can be calculated as follows:

V = 40 * [ Pi*18 + (h-6)*sqrt(12*H - H2) + 36*arcsin(H/6-1) ]

You will need an enginering calculator capable of doing arcsin function. To convert from cubic feet to gallons, you'll have to multiply the result by 7.48.

Or you can use this chart for your convenience:

- Code: Select all
` H (feet) | V (gallons) `

-----------------------------

0,0 | 0

0,5 | 482

1,0 | 1347

1,5 | 2441

2,0 | 3707

2,5 | 5107

3,0 | 6616

3,5 | 8210

4,0 | 9874

4,5 | 11590

5,0 | 13346

5,5 | 15126

6,0 | 16919

6,5 | 18712

7,0 | 20493

7,5 | 22248

8,0 | 23965

8,5 | 25628

9,0 | 27223

9,5 | 28731

10,0 | 30132

10,5 | 31397

11,0 | 32492

11,5 | 33356

12,0 | 33840

---------------------------

By the way, the calculations assume that your tank is placed horizontally on a flat surface. If it is not so, your figures will be different.