Metropolitan Washington could solve its water problems for the next 25 years without building any expensive and controversial dams and reservoirs.

The solution, according to a study done at the Metropolitan Washington Council of Governments, is a combination of cooperation between local jurisdictions and better management of existing reservoirs.

Author-Daniel P. Sheer said that if the present reservoris were full at the beginning of a dry period, the area "would come through the worst drought . . . with 5 billion gallons of water to spare."

The problem right now. Sheer said, is that the reservoirs are used the year round, even during wet periods when billions of gallons of water flow unused down the Potomac.

Under Sheer's plan, the District of Columbia, Virginia would draw water from the Potomac during most of the year.In the summer, when the Potomac's flow is low, the reservoirs - with their 20-billion-gallon capacity would be tapped.

Sheer said that by using water this way ghrough the year 2000 and possibly beyond, the area could survive a 90-day drought so intense it would have only a one in 50 chance of occuring.

While Sheer's idea would eliminate the need for new reservoirs - a long-standing but stymied proposal for solving the area's water needs - it would require some new construction: a new water intake on the Virginia side of the Potomac, an improved intake on the Maryland side and some interconnecting pipelines between the river and the reservoirs.

All this would cost millions. The exact cost would be worked out in a detailed analysis of Sheer's study that has been proposed by Johns Hopkins University Department of Geography and Environmental Engineering.

Ideas similar to parts of Sheer's plan have been proposed over the years, and a couple of them - new and improved intakes on the Potomac - are awaiting only approval of the Army Corps of Engineers. Sheer's plan is likely to command the attention of area water officials because it offers a regional solution of water problems that will hold up at least until the year 2000 without requiring more reservoirs.

"It looks promising," said James J. Corbalis Jr., director of the Fairfax County Water Authority. "Some of Sheer's proposals have been considered over a period of time. But he is using more up-to-date figures on demand (for water) and dealing with more sophisticated management techniques."

Sheer's plan counts on Bloomington Dam, now under construction in Garrett County, Md., and due to be finished in 1981 or 1982, to add 100 million gallons daily to the Potomac at the critical low-flow period that occurs primarily during July and August.

The plan also assumes that there will be an agreement between the suburbs and the District on allocation of the river's water at low-flow. Maryland and Virginia have reached such an agreement, but the Corps of Engineers, representing the District, has refused to sign it because, it claims, the Washington water needs are not protected.

COG's water resources board will consider Sheer's proposals at its meeting today. Sheer is a planning engineer with the Interstate Commission on the Potomac River Basin, which deals with problems involving pollution, water supply and land use.