Extract fan for cooltube?

ok, well today i brought an EcoTechnic's Cooltube. im trying to conserve on the electricity bill so ive gone to B&Q and got a bathroom extractor fan to use with my cool tube. The tube itself is 6" wide but i can only aquire 4" ducting to fit it to the extractor fan ( the extractor fan cannot support 6" ducting either ). The cooltube, ducting and fan will run in a straight line.

will this be suitable?

ok so ive got it all set up and running, its working great. check out the pics

http://i43.photobucket.com/albums/e362/str4ng3_photo/P1010203.jpg
http://i43.photobucket.com/albums/e362/str4ng3_photo/P1010206.jpg
http://i43.photobucket.com/albums/e362/str4ng3_photo/P1010207.jpg

Cooling pretty good? home depot has the 6" inline fans for $28.

yeah coolings not bad, i have the extractor fan blowing air into its neighbor cupboard. my plants can go at least 6" away from my light, although i might invest in a proper in-line fan when i have my next crop as the fan does not work very well when its not running in a straight line.