The $3.1 million Providence Recreation Center opens tomorrow, the fourth major indoor recreation center to be built in Fairfax County and the second one on the Beltway.

Built and operated by the Fairfax County Park Authority, the Providence center is expected quickly to become the second-most popular recreation center in the county. The most popular is Wakefield Park, the first and still the largest sports complex in the 400-square-mile county.

The location of the Providence center -- next to Falls Church High School on Rte. 50 just inside the Beltway and in the midst of a large concentration of business and industrial office complexes in that area -- is expected to attract daytime as well as nighttime users to the facility.

It has a large year-round swimming pool, handball/racquetball courts, weight and exercise rooms, saunas, game rooms and snack bar.

Providence, like the Mount Vernon and Lee centers, has the capacity to add future indoor gymnasiums like the one at Wakefield, but none of the other Fairfax recreation centers has the huge outdoor sports facilities of Wakefield, located just outside the Beltway at Braddock Road.

Joseph Downs, executive director of the park authority, who gave a guided tour of Providence Monday to local civic and business groups, said he expects the new recreation center to attract about 250,000 users a year and make an annual profit of about $700,000.

Wakefield this past year had about 350,000 users and generated $1.2 million net profit, which the park authority uses to help defray the rising costs of its other park operations.

Both the Lee and Mount Vernon district centers, located in primarily residential neighborhoods, had barely enough users in 1981 to pay operating costs, Downs said. The $2.1 million Mount Vernon Ice Rink, which is under the same roof as the center's other facilities, has been turning a profit, however. It opened in 1978, about three years before the rest of the sports complex was completed.

To encourage noncounty residents to use the Lee and Mount Vernon centers, the park authority this fall dropped the $1 and $2 nonresident fees it had been charging. Nonresident fees will not be charged at Providence, although they will continue at Wakefield.

The general admission fee at Providence thus will be similar to those charged at Lee and Mount Vernon: $2 for general admission ($1.50 for children and $1 for senior citizens) and $6 and $8 an hour for use of the handball/racquetball courts.

On opening day, Providence will offer free hot dogs.

The hours at Providence will be the same as the new hours at Wakefield: 8 a.m. to 10 p.m. daily, with use of handball/racquetball courts beginning at 6 a.m. The hours at all recreation centers have been changed twice this fall and numerous other park cutbacks have been announced as the park authority has tried to cut costs and stay within its county budget.

The most expensive of the four recreation centers, the $3.3 million Lee center, which was opened in October 1980 on Telegraph Road and South King's Highway, so far is one of the least used. Its hours have been the most curtailed, with the center now open only from 2 to 10 p.m. on weekdays.

Wakefield, by far the largest recreation center indoors and outdoors, cost $2 million to build in 1977. The much smaller Mount Vernon center, which opened in February 1981 beside the ice rink, also cost $2 million.

Downs said this week the park authority rushed through the $3.1 million Providence center -- the land was purchased by the park authority only in 1979 -- "to try to beat inflation as much as possible."

The park authority also has plans for about 300 new park projects, including two additional recreation centers comparable to Providence, Lee and Mount Vernon.

The new projects would be financed with bond issue funds the authority hopes county voters will approve in a referendum next fall. Hearings on the proposed centers, and on their locations, will be held in February or March, Downs said.