It is called Horse Tail Falls, as it looks like a horse tail whenever flowing. As we rarely get 4 days without rain, it flows every week. It takes less than half a day to start flowing, and continues for a day after. There is a short walking track to the top, which is lovely as walks go. Unfortunately I enjoyed it and did not time it. Also there is supposedly a track to the bottom also.
Horse Tail Falls near Queenstown
The World of Waterfalls has been to this waterfall, which you can read about here.