Fourteen persons were rescued from the windswept Potomac River yesterday after their chartered houseboat split a seam and sank swiftly in about 20 feet of water near Mount Vernon.

The houseboat's passengers reportedly spent as much as a half hour in the water before being pulled aboard a Coast Guard boat and private craft, including the motor vessel Diplomat, an excursion boat whose passengers snapped pictures of the rescue.

"My whole life flashed before me," said one of the houseboat passengers, Elizabeth Kozee of Silver Spring. It was "a terrifying experience," said another, Sheila Katze of Atlanta, a non-swimmer who clung to a rope for a half hour before being pulled from the water.

The 44-foot houseboat, the Cinnabar, was one of two heading from Washington to Mount Vernon carrying managers of Answering Inc., a Washington-based telephone answering service, who came here for a meeting.

After encountering a storm near their destination, Katze said, passengers took refuge in the cabin as the boat was buffeted and "things started flying around."

Suddenly, she said, there was a knock at the cabin door and "someone handed us life jackets." Then, she said, "the bottom of the boat fell out . . . I didn't jump. There wasn't time. It went down so fast."

Fortunately, help was near. According to Katze, company vice president Richard McNamara, who was aboard the other boat, the Tara, went to the aid of company president Frances Bowman, who had been aboard the Cinnabar. A man from another nearby boat dived into the water to rescue another woman. Someone on board the Washington Boat Lines' Diplomat threw a rope to Katze. Unable to climb the steep sides of the excursion boat to its deck, she said she clung to the rope until finally taken aboard a 21-foot Coast Guard boat sent from Alexandria.

Once on shore, nine of the passengers were taken to Mount Vernon Hospital, where they were examined and wrapped in blankets until their clothing dried and they were released.

"I'm still cold," Kozee said last night, five hours after the 3 p.m. accident.