A 13-year-old girl was punched in the face and needed surgery for a broken nose in the most vicious in a series of violent incidents since Brooklyn’s McCarren Park Pool re-opened last month.

Eighth-grader Sara Puk told The Post the trouble began as she and two friends were splashing around.

“We were screaming at each other, but it was like playing around,’’ she said yesterday.

An older girl said something to her, which she didn’t understand.

When she asked, the girl yelled, “Shut up!’’

EDITORIAL: POOL PARTY

Trying to avoid trouble, Sara and her friends changed and left.

But when they passed through the exit, they found the older girl and four members of her posse waiting.

“We just kept on walking,’’ Sara said, recalling her actions on July 11.

“They started following us. I was trying to stand up for myself, I was like, there’s five of you guys there’s only three of us, we’re really little,’’ she said. “I was scared, it was five against three.”

One of the older teens got in her face and declared, “I’m going to hit you and I’m just going to walk away.’’

Sara and her friends started running, but the older girls caught up. One made a video, which was posted on YouTube.

One of bullies yelled, “Go get her!’’ Sara said.

That’s when Eva Hawley, 16, allegedly landed a right hook to her nose.

“She’s jumping up and down, hysterically, laughing,” said a source who saw the YouTube video before it was taken down.

The older girls then took off and Sara, holding a towel to her bleeding nose, sat on a bench.

The attackers came back, one of them ripped the towel away and laughed.

“You are a bad-ass bully,” a Hawley pal gloated. “You f–ked up her nose good.”

“They were tormenting her and laughing,” the source said. “The victim starts to cry and they are mocking her for crying.”

They finally left and Sara and her friends approached a parked ambulance, which took her Wyckoff Heights Hospital.

Doctors had to operate on her nose, which had bled for three hours

Hawley was busted after Sara recognized her at a festival at a local church and told her mom, who notified cops. She was given a desk-appearance ticket for misdemeanor assault.

Another girl, 14, was issued a juvenile report.

The attack is the fourth violent incident since the Williamsburg pool reopened on June 28 after a $50 million renovation.

On June 29, a brawl broke out when lifeguards told teens not to do backflips. Three days later, a cop was punched in the face. And on July 17, a punk battled lifeguards and an NYPD deputy inspector.

But the Parks Department has not acknowledged a serious problem.

“Summertime skirmishes among kids are unfortunate but nothing new,” Parks spokeswoman Vickie Karp said. “The park and pool are safe.’’

Local residents disagree.

“There’s just too much of a criminal element here,” said Tanya Reed, 27. “It’s a beautiful pool, but I would never take my 2-year-old daughter here.”

The violence has sparked memories of the bad old days.

“People should be grateful, but they’re fighting,” said a 69-year-old Greenpoint resident, who was jumped at the same pool in her teens. “It started all over again — it’s like the 1950s. It’s a darn shame.”

Additional reporting by Amber Sutherland