There's nothing more thirst-quenching than a watermelon cooler.
Remove rind and any loose seeds from watermelon. Place the flesh in a juice extractor, and process, extracting 3 cups watermelon juice.
Transfer juice to a large pitcher. Add the remaining ingredients, and stir to combine. Fill pitcher with ice. Garnish with watermelon and lime wedges. Serve.
If you're using a food processor to juice the watermelon, remove the rind and seeds, and process flesh until liquid. Pass the puree through a fine strainer, and discard pulp.