用服务器流式传输YouTube视频

YouTube and Vimeo are filtered in Iran, and we don't have any access to them, now I'm going to use some video on YouTube and Vimeo and show them to Iranian people. This means I'm going to make a bridge between Youtube and Iranian visitor of my website, I know PHP but I can't understand how can I do it?

Pipeline of script:
Stream one video file from YouTube with my server that is in America and show it direct to my visitor that is in Iran.