The Prince William County Board of Supervisors voted unanimously yesterday to spend $500,000 to build a ballpark in Woodbridge for the Alexandria Dukes professional baseball team, which plans to move there next season.

Each supervisor was then presented with a baseball cap, decorated with the letter "P," by Dukes owner A. Eugene Thomas. The Dukes, a farm team for the Pittsburgh Pirates, are expected to change their name to the Prince William Pirates after making the move.

The Class A baseball team, which signed an agreement with the county last week, plans to occupy the new stadium in Prince William's Davis Ford Park, just across the Fairfax County line, after it finishes this season in Alexandria's Four Mile Run Park.

Jim Spangler, Prince William's parks and recreation director, said the Dukes signed the agreement with the understanding that the supervisors would allocate the $500,000 for the site.

The money will provide a 5,780-seat stadium, with 2,000 of the seats under cover, 2,500 parking spaces, and locker rooms and administrative offices, Spangler said. Three softball fields will be built next to the stadium.

Supervisors dipped into a $4 million general fund the county reserves for special projects to finance the additions to the new stadium, said Supervisor G. Richard Pfitzner. The fund, money the county won in lawsuits years ago, is separate from the county's $600,000 contingency fund for emergencies.

A dozen representatives from county recreation groups, the Chamber of Commerce and the business community spoke in favor of the allocation before the supervisors' vote, saying the baseball team will add $700,000 to the local economy annually and make the county better known outside its borders.

Only one speaker at yesterday's public hearing, county resident Thomas J. Rotelli, voiced some doubt. "I feel like I'm watching a tremendous orchestration," he said. "I can't say I'm against it . . . but this does not serve the recreational needs of the people. There are people who live across from county pools and can't afford to use them."

Under the terms of the lease, the Dukes will pay annual rent of $3,000 plus 10 cents for every additional spectator once the season's attendance reaches 45,000, and 20 cents per person once it reaches 100,000. The park authority also will receive 5 percent of all concession revenues, including beer sales.

In another matter, the supervisors voted to file suit along with the county sheriff's office against the State Compensation Board in an effort to raise the salaries of the sheriff and his staff.