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Consider the filtration medium. Activated carbon has a ridiculously large surface area to volume ratio and while yes this system clearly cannot replace a home system it can undoubtedly effectively filter the air in a bathroom. This design was made on a small scale but could easily be scaled up by using a larger fan. You could build something to contain the carbon and attach it to the back of a box fan if you really wanted to.
Well the fan has a diameter of 4 inches(10.16 cm) so a cross sectional area of pi/4*10.16 cm^2 which is 81.07cm^2 so to find the volumetric flow rate you multiply this number by the velocity of the air which is unknown but you could ballpark it or estimate it using bernoullis equation (http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html). All and all this particular fan doesn't pull air through too rapidly but will circulate air throughout a small/mediums sized room or car over time.This design could also applied to a more powerful fan with more durable materials if one desired to do so
Also this particular filter has a larger surface area than that considering that its about the same size of the fan
Simple and Cheap Homemade Air FilterView Instructable »