The Alexandria School Board Voted last night to reopen the Cora Kelly Elementary School, whose closing three years ago because of flooding problems generated considerable resentment in the city's black community.

Board members cited progress of the $55 million Four Mile Run flood control project, now nearing completion, as justifying the reopening in the fall of 1980.

Although the school, in the Lynhaven area of the city, had been flooded in 1975, black citizens complained when the board decided to close it the following year, saying they believed the reason for the closing was the school's location in a black neighborhood.

The board, at the same time, had decided against closing the John Tyler school, which is in a white neighborhood.

Last year, the board decided to relinquish the Cora Kelly property to the city government, but community pressure forced it to reconsider.

In deciding last night to reopen Cora Kelly, the board also voted to close John Tyler Elementary, turning it over to the City Council, which has jurisdiction over unused school buildings.

Tyler Elementary is adjacent to Northern Virginia Community College, which for several years has expressed a desire to purchase it. Last night's action is expected to be a signal that the school is available to the community college.

Last night's vote to reopen Cora Kelly was 7 to 1, with board member Michael Mulroney casting the negative vote. Mulroney called the action "shooting from the hip" and said he still had received nothing "in writing" saying that the flood control project is being completed.

Shirley Tyler, board vice chairman, said the board had received a letter from city officials saying that the project would be completed this October. She also noted that the board agreed last year to raise the question of reopening the school when the project was complete.

Osborne Banks, a Lynhaven resident who is president of the John Tyler PTA, told the baord: "Thank God you have stood up for what you said you would do for us in the community."

The school board also received a report showing improvements in most areas of academic studies for the 6,794 students in grades 1 through 8. Officials praised the results, pointing out that fifth and sixth graders had achieved their best levels in five years, and that the 7th and 8th grade students had equaled national norms in reading, language arts and math, for their grade level for the first time since the tests were originated in 1973.