I used my TI 84+ Silver and Google to do the calculations.
I thought up 3 different ideas. One uses 3" PVC, another uses 4" PVC and the 3rd idea (which is less likely to be used) uses 6" PVC. It doesn't have to be Schedule 40 pipe or whatever since it's just the reservoir.
Here is what I came up with.
I used the cylinder volume equation. The actual volume of water in the backpack may be slightly larger because I did not include the fittings.
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3" PVC pack:
π * 1.5^2 * 12 = 84.82300165
Ans * 3 cyl = 254.4690049 cubic inches
that = 4.16999987 liters which = 1.10159742 gallons
4" Pack:
π * 2^2 * 12 = 150.7964474
Ans * 3 cyl = 452.3893421 cubic inches
that = 7.4133331 liters which = 1.95839542 gallons
6" Pack(bit overboard lol)
π * 3^2 * 12 = 339.2920066
Ans * 2 cyl = 678.5840132 cubic inches
that = 11.1199997 liters which = 2.93759314 gallons
If it were 3 cyl
1017.87602 cubic inches
which = 16.6799995 liters or 4.4063897 gallons
But who would carry 6" PVC on their back??? lol