Several of North America's finest professional squash players and many nationally ranked amateurs are competing in the 30th Annual Woodruff-Nee Tournament that concludes today at the University Club in Washington. For the first time in the event's history, entrants in the open division are vying for a significant amount of prize money. The winner's take will be $750, and $450 will go to the losing finalist.

Top-seeded in the category is 26-year-old Aziz Khan of the Khan clan, which has dominated the Norht American squahs scene since the early 1950s. Aziz, ranked in the top five on the pro tour, will face stiff opposition from David Page, last Year's winner, and Page's younger brother, Tom, the No. 1 amateur in the u.s/.

Unfortunately, fans who wish to see the best squahs ever played in this area cannot gain access to the tournament. The Universicy Club, which is private, has only 44 balcony seats available, some of which have an obstructed view of the four courts where the action takes place.

The stands will be filled by the 48 competitors in the tournament who want to watch and by the club's members who purchased reserved seats. As club pro Tom Lane explained, "The facility just does not have the capacity to seat the players, members and general wpectators."

By 1980, however, downtown Washington will have at least two nonexclusive squash facilities that will include 10 air-concitioned courts apiece. Each club will have glass-backed courts and enough room to accommodate several hundred spectators for exhibitions and for matches.

Currently, there are about 45 squash courts in and around the metropolitan area, half of which the public cannot use. Both the Capitol Hill Squash Club, which will be located one block east of the Capitol South subway station, and the Washington Racquets Club, being constructed as part of One Lafayette Center (a new office and retail complex) will be open to any individual wishing to join and will ask an initiation fee of from $35 to $50 plus an hourly court charge.

In New York City, where the trend toward commercial clubs began in 1974, 11 centers now flourish. Women account for 40 percent of the memberships and newcomers outnumber veteran players four to one.

Squash is not experiencig the dramaic growth that typified the recent tennis and racquetball booms, but Darwin Kingsley, executive director of the U.S. Squash Racquets Association, says that the number of participants in the sport has doubled in the last 10 years, with most of the growth coming since 1974.

Based on the sale of squash rackets and balls, says Kingsley, there are a half million squash enthusiasts in the U.S., of which 200,000 play two to three times per week at roughly 1,000 court lications.

Kingsley attributes the sport's growth to the "increased emphasis on individual physical fitness. Squash is always rated near the top of the aerobics charts. Businessmen can get a hell of a workout in 45 minutes, not possible with tennis and golf. It's not as cheap as jogging but it's a lot more fun."

Also contributing to the sport's increased popularity has been the development and acceptance of a ball called the "70 plus," which is smaller, softer and slower than the type of ball used previously. Beginners, who had a terrible time getting the hang of the game before, are now injoying themselves much more.

The businessmen who hatched the idea for the inexpensive, nonexclusive commercial squash clubs and the introduction of the 70-plus ball are making the game more accessible to the public. Squash is no longer the exclusive property of the Ivy League.

"No one knows for sure," says Kingsley, who was a school teacher for 25 years, "but squash probably originated in the 1860s from an English game called hard racquets, which was played on a cement court with a superfast little ball. Students at Harrow waiting to get the racquets court (three times as large as a modern-day squash court) picked up some broken racquets and a soft rubber ball and began hitting it against a wall."

Squash made its way to America in the 1890s and was first played at St. Paul's School in Concord, N.H. The four-walled, standardized court used in the U.S. is 32 feet long, 19.5 feet wide and is about 16 feet high. The American court is 2.5 feet narrower than the English court, on which international squash is played, and the English ball is slower than the one used in America.

In the early 1950s the legendary Pakistani, Hashim Khan, first entered squash tournaments in the U.S. and started American players with a mastery of the game they had not dreamed possible. Hashim and his sons, nephews and cousins have created a dynasty in the would of squash that is unparalleled in any other sport. The Khan clan has dominated the game in North America, with very few exceptions, since Hashim's arrival.

Early in the 20th century, members of the Khan family were employed as ball boys at tennis clubs in India run by the British. As squash came along, the British sent some of their top players to India, then a British colony.

Hashim soon developed his game to a point where he was wiping out the British. In 1949, he was sponsored by Pakistani International Airlines, went to England and won the British Open the first time he entered.

There is now a growing crop of talented Americans on the squash scene. Twenty-five-year-old David Page, who runs three commercial clubs in Philadelphia, ranks 21st in the combined pro-am ratings and his 21-year-old brother, Tom, plays on a par with Aziz Khan.