Cats are not big water drinkers. Your cat should drink at least around 20-30ml per pound of body weight a day. So a 10 pound cat would be around a 1 and a 1/4 cup a day.
To encourage good drinking habits, especially in a cat with UT problems I would strongly suggest a cat watering fountain. Cats LOVE fresh clean water. A fountain will help keep it circulating, cooler, and aerated. I have yet to see a cat that doesn't like one of these.
You can find them a many pet supply stores, including pet smart.
Get one that filters the water and keeps it moving all the time.
Let me know if you have any other questions.