The Prophet (may Allah's peace and blessings be upon him) used to run the water around his elbows while performing ablution
Authentic hadithعن جابر بن عبد الله رضي الله عنهما قال: كان النبي صلى الله عليه وسلم إذا توضأ أدار الماء على مِرْفَقَيْهِ.
Jābir ibn ‘Abdullāh (may Allah be pleased with him) reported: The Prophet (may Allah's peace and blessings be upon him) used to run the water around his elbows while performing ablution.
Explanation
This Hadīth indicates that among the obligations of ablution is to wash the hands up to the elbows. Stressing the necessity of washing the elbows thoroughly indicates that they are included in the washing of hands.
Source · Al-Bayhaqi - Narrated by Ad-Daraqutny
From the Hadith Encyclopedia (hadeethenc.com).