By Jeb Blount

RIO DE JANEIRO (Reuters) - Brazil won its first medal of the Rio Olympics on Saturday, but its hard cheering fans also suffered deep disappointment as a top gold-medal hope was eliminated from the judo competition, left in tears on the mat with a dislocated elbow.

After months of criticism over construction delays, corruption, safety and polluted water, Brazilians were out in force to support their teams. They were buoyed by an opening ceremony on Friday that spoke directly to their complex and rich history and culture and eased local anxiety that the Games costing nearly $13 billion might founder.

Enthusiasm turned quickly to shock for many home team fans though. Brazil's Sara Menezes, a judo gold medalist in London in 2012, was rushed to hospital after being eliminated in a bruising match against Mongolian Urantsetseg Munkhbat to finish seventh.

Judo is one of Brazil's most successful Olympic sports. But Menezes was in such pain after having her arm yanked in the match that she was unable to get up to acknowledge her opponent's traditional bow.

Another Brazilian judo contender Felipe Kitadai, also cheered on by name by fans, was also eliminated in the men's 60kg Judo class by Uzbekistan's Diyorbek Urozboev. Kitadai finished seventh.

Still, Brazil's Felipe Wu made a good start toward the host country's goal of breaking into the top-10 total medal count for the first time. He won silver in the men's 10m air pistol event after being edged out for the gold by Xuan Vinh Hoang of Vietnam.

On a glorious, sun-drenched Rio de Janeiro day, Brazilians filled stadiums and streets and lined rowing and biking courses, shouting themselves hoarse alongside thousands of visitors from around the world.

"It's not like we don't know there are problems, if anybody knows that we Brazilians do," said Kele Fermino, a Rio real estate agent shortly after cheering on the bicycle road racers at the bottom of a steep descent in the Jardim Botanico neighborhood.

"The opening ceremony was wonderful, hit all the right notes and today is beautiful," she added. "We Brazilians, the people, we embrace our athletes totally despite all the problems, and we are convinced that we are going to have a good time at the games."

That spirit was evident at the men's gymnastics team qualifying event, where Brazil's team qualified for the men's finals.

During subdivision matchups with Japan, Korea and the Netherlands, chanting, singing local crowds, and a couple of emotional athletes' mothers, gave it their all in trying to spark Brazil to victory.

While Brazil has recently developed several top-flight gymnasts including Arthur Zanetti, 2012 gold medalist in rings and multiple world champion Diogo Hypolito, it has never before qualified to compete for a team medal at the Olympics.

Hypolito broke down in tears after helping Brazil come in second to historic powerhouse Japan before later rounds moved them to sixth behind China, the United States, Russia, Japan and Britain. Only the top eight teams qualify.

Similar scenes played out at the beach volleyball, fencing, and judo, and swimming venues, though the results in competition were mixed.

Brazil's women's double of Agatha and Barbara beat the Czech Republic's Hermannova and Slukova 19-21 21-17 15-11 at a packed beach volleyball stadium on Copacabana Beach. Crowds were riotous despite long lines and delays at security gates. Hundreds without tickets cheered from the street and on the sand nearby.

Willy Pereira, 28, a computer technician, wearing a Brazil shirt as he stood in line for the matches Saturday morning explained the love cariocas, as Rio residents are known, have for the sport.

"In Brazil, first it's football and second it's volleyball. I'm carioca, I love the beach. I play volleyball ... on this beach or in Ipanema. It's a marvelous sensation to have this so close to home."

Brazil's first appearance in the quarter-finals of women's fencing ended there. Nathalie Moellhausen brought Brazil its first ever quarterfinal fencing appearance in Women's Épée only to be eliminated by France's Lauren Rembi 15-12 to finish sixth after Brazilian fans livened up a traditionally restrained sport.

Brazil put three swimmers into semi-final races. Daynara de Paula, won her heat in the women's 100m butterfly and qualified in 14th place, while Daiene Marcal also squeezed through tying for 15th. Felipe Franca qualified in third for the men's 100m breaststroke.

The Brazilians even whooped it up at the Table Tennis event, though the cheering may have contributed to the elimination of Brazil's Caroline Kumahara. She fell short of the second round after a loss to Luxembourg's Ni Xialian 4-3.

During the match, the audience stomped, chanted Caroline's name and also booed Ni once when she was serving, a situation largely unheard of at ping-pong tournaments, Kumahara said.

"It was a little bit bad," Kumahara said, referring to the times when she said she could her fellow Brazilians screaming.

(Reporting by Jeb Blount; Additional reporting by Brenda Goh, Mark Trevelyan, Alexandra Ulmer, Brad Haynes and Liana Baker; Editing by Tom Brown)