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Math super genius help please!

Thales

Thales

Past President
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I am setting up a 240 gallon tank for salt mixing at home (thanks Gresh!). I have calculated volume based on 1 inch increments - see below. However the tank is not level. I know, I should level it, but thats not going to happen for a while and I need some water soon. :D The inside dimensions are 23 inches x 95 inches, and the slope is in the long direction giving a 1/2 inch difference from one side to another. So, on the short side near the access door, the water is currently 13 inches deep, but 95 inches away on the other side its 13.5 inches deep.

My question is how would you calculate accurate volume in 1 inch increments on the shallower side, taking into account this slope?

Does that make sense? If not please ask me questions. :D I do have my own ideas, but since I am not at all a math genius, I thought tapping the giant BAR brains would be a good idea.

Thanks!




1 9.46
2 18.92
3 28.38
4 37.84
5 47.3
6 56.76
7 66.22
8 75.68
9 85.14
10 94.6
11 104.06
12 113.52
13 122.98
14 132.44
15 141.9
16 151.36
17 160.82
18 170.28
19 179.74
20 189.2
21 198.66
22 208.12
23 217.58
24 227.04
 
How accurate do you want it to be?

Very close accuracy puts that first "inch" of water at 3/4 of the volume if it were level. One side would be at 0" when the other side was at 1/2" so it essentially makes a triangle cross section, which is 1/2 the cross sectional area of a rectangle (i.e. if it was level). The next 1/2" is is just a full 1/2" worth of water, so 3/4 for that first inch, then each inch after would be 1" worth of water.

Now there could be a slight variation because the sides are sloped, however that shouldn't make that much difference over the whole tank.
 
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