For Alexandria City Council members Beverly Beidler, the failure of metropolitan Washington to develop a regional solution to its mounting water problems was emphasized intwo vividly contrasting experiences she had yesterday on her way to a "water supply summit" meeting in downtown Washington.

"When I went out the front door of my house, I saw grass that was brown because I can't water it during the water restrictions in Alexandria. Coming to this meeting, I walked past green lawns in Washington that were being watered by sprinklers. Some of the water was flowing, unused, along the street."

The sprinklers are working in the District because it uses the Potomac River as a water source, and though the river is flowing at its lowest rate in 11 years, there is still enough for the more than 2 million people in the area who depend on it.

But Mrs. Beidler and the other 115,000 residents of Alexandria, along with almost 500,000 people in Fairfax and Prince William counties, depend on the Occoquan Reservoir, which ahs dwindled to about one-quarter of its usable storage.

While lawns go brown and cars go unwashed in the Occoquan service area, with the possibility of sharper restrictions in coming weeks, billions of gallons of water flow unused every month down the Potomac.

This was one of the predicaments taken up at yesterday's water summit, sponsored by the Metropolitan Washington Council of Governments and nine other local agencies and organizations.

There was a lot of talking at the summit, just as there was at the 17 public hearigns on regional water problems that were held in the area earler this summer. But for the first time, all the jurisdictions - the ones still enjoying a surplus of water and the ones rationing their dwindling supplier - agreed on an "action program" that could lead to a regional solution that would hold up for 20 years or more.

Adopting motion offered by John F. Herrity, chairman of the Fairfax Board of Supervisors, the summit agreed to:

Expedite negotiation of an agreement on allocation of Potomac River water when demand exceeds supply because the flow of water in the river is low.

The Army Corps of Engineers, one of the assenters to the agreement, has been insisting on such an agreement before agreeing to grant the Fairfax County Water Authority a permit to tap the Potomac as supplementary water supply. The corps says it wants to protect the District's supply far into the future when demand on the river will be much of greater.

Expedite analysis of a proposal by engineer Daniel Sheer of the Interstate Commission on the Potomac River Basin to connect local reservoirs with the Potomac. Sheer said connections will increase the reservoirs' storage potential, climinating the need for new dams up to the year 2000. and perhaps beyond.

Expedite analysis of engineer Noman M. Cole Jr.'s plan to increase the Occoquan's capability by pumping water to it from the Shenandoah River near Front Royal, Va.

Submit to Congress and President Carter a request for federal funds to finance projects such as reservoir river connections.

This may be the most questionable possibility in the plan. The federal government traditionally has not paid for water-supply projects.

Encourage uniform measures through the region to reduce demand.

THis was a victory for conservation advocates who have been arguing that too often proposed supply projects assumed unlimited demand, and thus were on a massive, expensive scale.

The summit also adopted another motion, also offered by Herrity, that establishes a water supply steering committee that will include all the local governments and other key agencies and organizations. Such as the Corps of Engineers. The committee will hold another water summit in May, 1978. to see how much progress has been made on the action plan.

"We have to do something now." COG board chairman Harold L. Miller, mayor of Falls Church, told the audience. "The decisions to be made are political decisions . . . But the only way to get the political decisions made is to get the public to stand up and say we've had enough, let's get going."

There were more public officials at the meeting than ordinary citizens. More of the citizen comments were from advocates of limited growth. Charlottee P. Gannett, representing the Montgomery County Environmental Coalition, a slow-growth group, said. "No one in the metropolitan area assumes responsibility for finding out where the pollution (upstream) comes from and trying to abate it."

She also defended the Corps of Engineers, whichhas often been anathema to environmental groups. But because the corps is holding up construction of an intake on the Fairfax side of the Potomac and another project on the Montgomery side until the District's needs are assured, the colonels and generals of the corps are wearing white hats as far as some environmentalists are concerned.