Fan affinity laws from a collision model
  The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour of air is incorporated. Our calculations prove the affinity laws and provide numerical estimates of the air delivery, thrust and drag on a rotating fan. 
Shayak Bhattacharjee
physics.class-ph