Two Fans One Duct

2 bathroooms lead to the fan then exit through one pipe out the roof.

Two fans one duct.

2 backdraft dampers one on each leg at the y to stop the backflow of noxious gases from one fan on to the other off. Total pressures are used instead of static pressure because the fans can actually be different sizes and a change in fan or connecting duct areas has an influence upon static pressure values. There may also be bypass ductwork around the second fan if only one fan is run for a period of time. This setup requires an in line centrifugal fan mounted in the attic drawing air simultaneously from both bathrooms see photo.

Rather than two cheap axial fans into one duct outlet how about two ducts into a more powerful centrifugal fan which is a bit more expensive but has a lot more oomph. Note that the backdraft dampers will add to the resistance of the duct work. If you try to combine them into a common duct it will bring with it a number of problems including an unbalanced system with positive negative air pressures which play havoc with the fan motors and could cause motor failure. The problem as i understand it is that if both fans are using the same duct and are both running at the same time the fans will be less efficient and more noisy because it will be like installing a fan with a smaller duct that it was rated for.

You may wish to move up to the next size of duct. You should not put more than one fan into a common duct each fan should have its own duct run to atmosphere. I think it may be possible to arrange for one fan to suck air equally from two inlets. Of course there is some issue with the volume of air from 2 ducts going into 1 duct but i m sure some engineer has figured that part out.