(Recasts with state of emergency, latest forecasts)

HONOLULU, Aug 13 (Reuters) - The island of Hawaii declared a state of emergency, closing schools and setting up shelters, as Hurricane Flossie approached the Pacific state's southeastern waters.

Flossie weakened from a Category 4 to a Category 3 at midday Monday, but remains a "dangerous hurricane with a clear, well-defined eye," according to the National Weather Service's Central Pacific Hurricane Center.

Flossie's strength is not expected to change over the next 24 hours, it said.

The service put the island of Hawaii under a hurricane watch early Monday and said Flossie would come within 85 miles (140 km) of the so-called Big Island around 2 p.m. local time (8 p.m. EDT) Tuesday.

Winds at that time will be at 40-50 miles per hour (65-80 km) and surf will exceed 15 feet (5 meters). Torrential rainfall of up to 10 inches (25 cm) is expected along the southeast shore, said Ray Tanabe, National Weather Service warning coordination meteorologist.

Island of Hawaii Mayor Harry Kim issued a state of emergency Monday afternoon for the volcanic island's population of 160,000. "We're taking this all very seriously," said Janet Snyder, Kim's press secretary.

For the rest of the state, the main impact will be high surf along shores facing south and east, Tanabe said.

"All the islands of Hawaii are at equal risks for hurricanes," Tanabe said. "There is still a chance the hurricane could take a jog a bit to the north, but it has been fairly well behaved."

The weather service has also issued a flash flood watch.

The last recorded hurricane to hit the island of Hawaii was the Kohala Cyclone in 1871, Tanabe said. More recently, tropical storms Estelle and Jimena both passed south of the island of Hawaii in 2004 and 2003.

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