With a little help from its friends, the U.S. National Arboretum gained a Washington version of an Asian mountainside garden last week when a 150-foot waterfall began to gurgle down a high bank of the Anacostia River there.

The waterfall is the $80,000 gift of Mrs. Randolph Kidder, wife of the ambassador to Colombia in the Johnson administration and a member of the newly incorporated Friends of the National Arboretum.

The friends--so far there are only nine--already have funded an expedition Japan that is collecting more plants for the waterfall garden. The garden now boasts banks of Asiatic plants and a large, red Chinese pagoda, donated in 1950 by the Garden Club of America, and will have hundreds more plants when it is dedicated formally next year.

The group also hopes to begin a ferryboat service from a dock at the foot of the waterfall to the Kenilworth Aquatic Gardens across the Anacostia, where the National Park Service is planning a boardwalk and dock at its waterlily gardens. Rangers will mark the Kenilworth gardens' 100th birthday Saturday with special tours of the park's 11 acres of exotic and native water plants.

With other outside gifts, the arboretum is expanding its popular bonsai pavilion, which houses a $4 million collection donated by Japan during the Bicentennial. This fall, a special bird and butterfly garden, filled with trees and plants that attract these creatures, will be dedicated at the arboretum.

Officials also are negotiating for donations to create a National Vegetable Garden "that would bring the big tomato to the arboretum," said Henry Marc Cathey, who is completing his first year as arboretum director.

Private donations have become crucial to the arboretum. Its budget from the U.S. Department of Agriculture has been almost static for several years, except for extra maintenance funds to repave the 10 miles of arboretum roads and to erect fences for better security.

At the new waterfall, a 1,750-gallon-a-minute pump recycles the brackish purple water through underground pipes to the top of the falls. The water color is from an antialgae solution that also serves to deter swimming in the three-foot deep pool at the bottom.

"No one wants to come out stained with purple dye," Cathey noted.