The centerpiece of Vermont’s new mental health system is up for a public hearing on Friday. Closure of the old Vermont State Hospital in Waterbury by flooding from Tropical Storm Irene forced the state to come with a new plan to care for the mentally ill. It has been developing a system that would include small psychiatric units in several different parts of the state, plus a 25-bed facility in Berlin. The Berlin facility now is working on getting a permit called a certificate of need from the state Department of Financial Regulation. The department will conduct a hearing on the application Friday at 1:30 p.m. in the third floor conference room of 89 Main St. in Montpelier.