Best solution is to find the model of your old backpack and look up the specs online ...

Failing that, I don't know. If you can reuse the water afterwards for watering plants or something, getting a contractor bag and filling it with water could work, then measuring out the water in whatever measuring devices you have available (a funnel and gallon jugs if nothing else). Awkward/heavy, though, and could get wet/messy ...

To get in the ballpark, at least, stuff it full of whatever --- clothing, newspaper, etc, and take external measurements to get at least a reasonable approximation.

Kind of a fun challenge!