Prune juice for constipation

So my 3 month old has been constipated and when he has pooped it’s been hard and painful for him. The doctor recommended prune juice for him. I bought the sunsweet amazin 100% prune juice. I mixed 2 ounces of baby water with 2 ounces of prune juice and gave it to him. Is this appropriate? How many times should I give it to him? I have him his first round of the juice about an hour and a half after his feeding so his little tummy isn’t so full. How quickly will it work?