The Sony HDR-SR10 does not support "USB streaming" so using it as a webcam via USB is not an option.
It should be possible with an HDMI capture card like this one:
http://www.amazon.com/Blackmagic-Des.../dp/B001CN9GEA
Take a look at this review:
http://www.amazon.com/Blackmagic-Des.../dp/B001CN9GEA