Exactly, I would like to math before hand . I am just wondering how can I make the math :)
The maths is extremely simple and also pretty much impossibly complicated.
At a basic (pun only semi-intended) level, the pH of a solution is given by the negative base-10 logarithm of the hydronium ion concentration, i.e. pH = -log[H3O+]
Looks relatively simple, doesn't it?
But now you have the problem of calculating what the concentration of hydronium ions is. Even if you start with a relatively "trivial" case of a single simple acid or base, where you can reasonably look up the dissociation constant, your water source will likely have more than just pure H2O in it. So you've then got to account for the effective of these other soluble solids, and before you know it, you've got a very complex (from the perspective of calculation) system.
And then you want to add a juice to that. So we have to ask, "what is in the juice?", i.e. can you chemically define it to a sufficient degree? There is a reasonable amount of published literature on the composition of juices, but you need this data for your specific batch, so you're into the realms of some pretty involved and specialist analysis. Even if we assume that you're lucky to have access to a $millions of lab facilities that can do all of these tests, you've still got to try to do something useful with the data at the other end. So once you have this compositional information, you have a combined system of water, citric acid, other things in the water, and the hundreds/thousands of different components of the juice, and somehow you've got to put that into your calculations to determine what the actual effective hydronium ion concentration is.
I genuinely think it could be quite an interesting exercise, but it's not one I'd want to undertake unless I had access to a reasonable number of chemistry PHD students and a decent supercomputer or two. If you're exceptionally well-versed in chemistry then there are probably some reasonable simplifications and assumptions you could make to reduce the complexity of the problem, but I still think it'll be a remarkably ineffective approach.
TL;DR: I agree with everyone else here - testing with a pH meter is the approach to take. You may find over time that you notice broad patterns in terms of x amount of juice tends to change the pH by y +/- a bit, and can use that to save yourself a bit of time having to do so much trial and error, but you'll also observe that even after many batches it'll not be entirely precise. And then the crop season will change and your juice might do something unexpected randomly anyway 
