Seen from the air, the West seems virtually empty. But the perfect circles of dazzling green, like cut emeralds in sand, produced by huge circular irrigation sprin klers, suggest how much emptier the West would be but for irrigation. Parts of the West, urban and rural, including the high plains, may be, in a sense, overpopulated, considering the problem of organizing sufficient water.

In a fascinating new book, "A River No More," Philip Fradkin explains that the Colorado River, which is "the Nile of America" in its role as "unifying source of life in the West," is at the core of a "complex plumbing system" that sustains an "oasis civilization" that will wither if (actually, he says when) shortages come.

The Nile extends 4,000 miles and has an annual flow four times that of the Colorado, which extends just 1,700 miles and has a flow equivalent to that of the Delaware. But even more than the Nile, the Colorado is a prodigy of life-giving.

It has the warmest water, highest evaporation rate and biggest silt and salinity ("hardness"--the accumulation of dissolved minerals) problem of any American river. The salinity increases 17- fold between the headwaters in Colorado and Wyoming and the Mexican border.

For 20 years, not a drop of the Colorado has reached the river's natural outlet in the Gulf of California. Similarly, the Gila River, which used to join the Colorado at Yuma, Ariz., now falls short by about half of its former 600-mile length.

The river that sustains the West sustains, above all else, the artifact at the center of American civilization: the hamburger. Ask not for whom the river toils. It toils for cattle.

In the upper Colorado basin, 60 percent of the land is federally owned; in the lower basin, 52 percent. In Nevada (86 percent), federal holdings are twice the size of New York. In California, they are eight times the size of Massachusetts. In Utah, they are the size of Florida. And nearly 250 million of the 350 million federal acres--an area larger than the Atlantic seaboard states--are administered for grazing.

Since 1950, irrigated acreage in the high plains has septupled as the region, responding to postwar America's ravenousness regarding red meat, has become the principal supplier of feed grains and feed-lot cattle. Livestock feed is raised on 88 percent of the 1.6 million irrigated acres in the upper basin. Of 99 million acres in the lower basin, 82 million are range land or pasture.

In 1975, irrigated agriculture--principally alfalfa--consumed 7.5 million acre-feet of water in the Colorado River basin. Evaporation took 2.3 million and industrial uses (including power plants and mining) took just 630,000. Newsweek reports that if you count (and you should) the water that irrigated the grain that was fed to the steer, the steak on your plate may have required 3,500 gallons of water. The water needed to produce a 1,000-pound steer would float a destroyer.

Out here, where a bumper sticker says "Support Beef--Run Over a Chicken," cattlemen face hard times. Prices, and concern about health hazards from fatty red meat, are causing consumers to consume more chicken, pork and fish. Since the peak year of 1976, beef consumption has fallen from 95.7 to 78.3 pounds per person annually.

Conservative ideology and western regional loyalties are in entertaining tension in the Reagan administration, so it is unlikely that beef will be made less competitive by the government imposing the principle of "full-cost recovery" on water users.

Nine of the 11 western states have population densities much lower than Maine, the least dense state east of the Mississippi. But for the first time in 50 years, most of the West's population growth is happening outside California. It is happening within the Colorado River basin, and most of the West's population now is directly dependent on that river.

As Fradkin says, the West was not won by the six-gun but by shovels-- shovels that moved dirt so that water could be moved. The federal government, much reviled in the West, has been skillfully milked by the West for the reclamation projects on which the region has depended.

As Bernard De Voto once wrote, the attitude toward the federal government has been "get out and give us more money." But there are limits-- and they may be near--to what even well-funded ingenuity can do to multiply the usefulness of scarce water.