The Fairfax Board of Supervisors, which has been frustrated in many attempts to gain control over development in its fast-growing county, moved yesterday to set stricter limits on the size of new sewer pipes.

By 8-1 vote, the supervisors approved a public hearing on a measure sought by Audrey Moore (D-Aanandale) that would limit capacity of sewer lines to the maximum population permitted under the county's comprehensive master plan, based on the zoning for each parcel. The measure would eliminate the present flexibility the county staff has to approve construction of larger pipes to accommodate more population growth than specified in county plans.

While the vote yesterday merely authorized a public hearing on the measure, it was clear a majority of the board supports the stricter limits on size of sewer lines.

"We have been beating our heads against the wall to get state legislation to control growth," Supervisor Alan H. Magazine (D-Mason) said, summarizing the sentiment of the majority. "If this is the only way to slow down the growth rate, then I am for it."

The availability of sewer, either in the pipeline or at the treatment plant, is one of the chief factors affecting rate of development. Tighter restrictions on pipeline size would presumably give the supervisors some of the control over growth that they have not been able to obtain in other areas.

In its action, the board overruled County Executive Leonard Whorton, who wanted his staff to continue to be able to approve sewer pipelines in dimensions greater than those called for in present guidelines.

The guidelines, contained in th county public facilities manual, call for pipes designed for a population density not less than 10 persons per acre, even though the master plan or existing zoning may call for a lower density. Additionally, the guidelines say county staff members can design large pipes when they are "deemed necessary."

The new limit favored by the supervisors would not curb any of the considerable potential for growth permitted under the county's comprehensive plan. Under that plan an subsequent rezoning, hundreds of thousands of people could be added to Fairfax's population of 565,000 over the next eight years, with the growth rate limited only by housing market conditions.

But the new sewer line limit, by taking flexibility out of the staff's hands, would tend to rule out exceptions to the master plans to allow higher densities. Elimination of the 10-persons-per-acre minimum would also tend to rule out revisions of the master plan permitting higher densities.

Since 1972, supervisors have attempted in a variety of ways to gain more control over growth. Primarily they have sought to phase-in growth by controlling when construction of schools, roads and other public facilities occurs and when services are provided that residents either require or demand.

Most of the growth pains in Fairfax - the most rapidly developing jurisdiction in the metropolitan area in the 1970s - have resulted when public services and facilities lag behind new population.

But Fairfax has been unable to get legislation approved by the State General Assembly that would give the county clear-cut power to phase growth.

In other actions, the supervisors:

Approved a recommendation by Whorton that Fairfax pay its $382,790 share of the debt payment on Metro revenue bonds, which were sold to meet the escalating price of completing the planned 100-mile subway system.

Declined to grand a special exception to Bowl America, Inc., so the company could expand a parking lot onto residentailly zoned land near Herndon Junction on Rte. 228. While the popular bowling center is in Loudoun County, additional land planned for expansion is in Fairfax.