While black colleges across America are running scared--wondering whether they can survive the Reagan administration cuts in student aid, shrinking enrollments, deficit-ridden budgets and the talent drain, as the brightest students and faculty are lured off to white schools--Hampton Institute's young president exudes confidence.

"Things are going well with us right now," says 40-year-old William Harvey, savoring the understatement.

Enrollment, which was around 2,600 four years ago, has topped out at 3,450-- about as much as the school can handle, Harvey says, even with the new 300-bed dormitory now under construction. Average Scholastic Aptitude Test scores of entering freshmen are up some 66 points, bucking a national trend for colleges, black and white. Hampton ranks as the most selective black college in America. And, for the fourth year in a row, the 114- year-old school will finish the year with a surplus in its $25 million budget.

"Things are going well with us," Harvey says again, this time with just a hint of a boast. "These things don't just happen," he says. "You don't just throw things up in the air. It takes planning. You have to have goals, and strategies for reaching them."

His first goal, when he came to Hampton in 1978 (after administrative stints at Harvard, Fisk and Tuskeegee) was to get the Tidewater Virginia college on a solid financial footing. "I inherited a $486,000 deficit on a budget of $18 million. Only one year in the 1970s was Hampton in the black. My very first year, we ended with a $44,000 surplus."

How did he manage it? "Well, we started with a good foundation: our alumni contribute more than at any other black college in the country--more than $400,000 last year. That helps us in our corporate fund-raising."

It also helps that Harvey has been able to attract some important people to serve as trustees. "Hampton has always had movers and shakers on its board--people like Eastman, Rockefeller, Du Pont. The same is true now. We've got people like Bill Ellinghaus of AT&T, Gov. Chuck Robb, former Gov. Linwood Holton, John Duncan of St. Joe Minerals, Jack Dorrance, chairman of Campbell Soups, Sam Pierce, Elizabeth Taylor--these are people I've gotten since I have been here.

"But the main thing is what you might call supply-side economics at the university level. People need to know that they're not giving money to support red ink, that they're not supporting ineffectual programs, that they aren't giving money to some shabby, run-down college. They are giving money to a place where it's doing some good, where it is making an impact."

Thus a major part of Harvey's fund- raising strategy is to get potential benefactors to visit the campus for a firsthand look at Hampton's academic success. It works, he says. "Just a couple of weeks ago, we got a $500,000 grant from the Gulf Oil Co. to endow a chair in chemical engineering. A week later, we received $150,000 from Connecticut General."

As with other aspects of Harvey's administration, the academic improvement doesn't just happen. It is true that some of the brightest black students are attracted to the campus, partly because of its reputation, partly because of its social environment and partly because of its setting: a 200-acre peninsula jutting out into the Hampton River, in a metropolitan area with the lowest crime rate in the state.

But Harvey also sweetens the scholastic pot by granting scholarships to students who score above 1,000 points on their combined SAT scores.

"We are promoting Hampton as the quality alternative (to predominantly white colleges)," he says. "We nearly always have five or six sons and daughters of black college presidents among our students. Eighty percent of our students are high achievers, many of them from college-prep schools, and the other 20 percent, accepted as a matter of school policy, get special catch-up help.

"A lot of black students are interested in attending a predominantly black school, partly because they are at the age where they will be choosing their husbands and wives. But they also need to know that they will not be sacrificing on the academic end."

At Hampton, they've got it both ways.