The water added really depends on how big your pot is and how many vegetables are in it, to "add to cover" so it depends each time. You can always eliminate the water completely and use vegetable broth for all your liquid instead.
If you like measurements, rather than 3 potatoes, for example:
2 cups diced potatoes
2 cups diced beats
(But truly, when making soup it's really a little of this a little of that so you don't need to be too precise!)