The damaged engine can be seen in video a passenger tweeted from United Airlines Flight 1175.
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The flight took off from San Francisco International Airport just after 12 p.m. ET and landed at Honolulu's Daniel K. Inouye International Airport at 5:42 p.m. ET.
The aircraft involved is a Boeing 777. It has two engines and is designed to fly on just one engine for more than three hours over water.
Here are more tweets from that passenger:
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An engine cover came off during its flight from California, the airline said.
"Our pilots followed all necessary protocols to safely land the aircraft," United said in a statement, adding that all passengers departed the Boeing 777 normally at the gate.
The airliner landed as emergency responders waited nearby, said Hawaii Department of Transportation spokesman Tim Sakahara.
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An emergency was declared due to a vibration in the right engine, said Federal Aviation Administration spokesman Ian Gregor said in an email.
The FAA will investigate.
(The Associated Press contributed to this report.)
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