Members of the Vienna Town Council approved with ease an increase in the town's water use rate Monday night, but wrestled long and hard with the problem of which comes first, public or private interests.

Water charges for in-town customers will go from 85 cents to 92 cents per 1,000 gallons of water used beginning July 1. Vienna's fiscal 1985-1986 budget was passed June 3 on the condition that the new water rate, which will also add 9 cents to out-of-town customers' current rate of $1.13 per 1,000 gallons, be set at the next council meeting.

Town Manager John Schoeberlein said despite the increase, estimated to raise the average customer's yearly water bill by $5.60, Vienna water customers will still pay well below what residents of Fairfax City, Falls Church and Herndon pay for water.

Before setting the new water rate, the council tackled two thorny problems of public versus private interests. In the first case, William Donnelly told the council that his family had lived in Vienna just a week when they found their house flooded with sewage from the town's waste system. He requested that the council reimburse him $1,100 for a carpet that was removed from his home during the cleanup.

But the town's insurance carrier has invalidated the claim and Mayor Charles Robinson said, "Until we have some evidence of protected liability we're not setting a precedent we can't live with."

He instructed Schoeberlein and the town lawyer to look into the possibility of "no fault" insurance to cover such liabilities in the future. The council deferred the matter until August.

n the second case, Frank Kormann asked the town to assume some responsibility for the maintenance of a private pond that is part of the town's storm drainage system. Kormann, owner of the Delilah Drive property on which the man-made pond is located, said that dredging of the pond and repair of its drainage system could be done at a cost of $11,500.

Robinson said the pond rehabilitation costs should be a "shared responsibility" because the pond, though originally built for private esthetic purposes, had been co-opted as part of the town drainage system.

"I don't think there's any benefit to the town of having a pond there at all," said council member Rodger Seeman. "There is absolutely no benefit . . . because it has no benefit downstream. The town doesn't have the right to spend money on a private duck pond."

Council member George Lovelace disagreed, saying that the problem should be solved "once and for all. As long as it's part of our storm water system, we have a responsibility to clean it up."

But Seeman, who had questions about the engineering specifications concerned in the cleanup, and council member Robert Robinson succeeded in getting the council to agree to look at the pond situation again at a work session in July.

Mayor Robinson agreed to the deferral, but not before telling Seeman, "The major engineering factor is that water is responsible to the law of gravity."

Among other council actions at Monday night's meeting: Newly elected council member Richard Fisher, who currently heads the town planning board, and reelected council members Robert Robinson and Rodger Seeman were sworn in for two-year terms. The council approved a donation of $1,000 to the Marshall Road School PTA for the purpose of installing air conditioning in the school. The selection of a consultant to conduct a traffic study was deferred until a July work session. The council voted to maintain a schedule for reimbursement to people who lose their homes because of condominium conversion that is in line with Fairfax County policy.